UC-NRLF 


kl\l.  1.11 


i^>^ii-.vi'Vf?§v;^f<?*i^-w<^«?wv*i?'i*wv5<5wi«)yw>i>^^ 


I 


IN  MEMORIAM 
FLORIAN  CAJORl 


INTERMEDIATE   BOOK 


^M& 


THE  MACMILLAN  COMPANY 

NEW  YORK    •    BOSTON  •   CHICAGO  •   DALLAS 
ATLANTA  •   SAN  FRANCISCO 

MACMILLAN  &  CO.,  Limited 

LONDON  •  BOMBAY  •  CALCUTTA 
MELBOURNE 

THE  MACMILLAN  CO.  OF  CANADA,  Ltd. 

TORONTO 


SCHOOL   ARITHMETICS 


INTERMEDIATE  BOOK 


,»   »  » .  > 


BY 


FLORIAN  CAJORI 


THE   MACMILLAN  COMPANY 
1915 

AU  rights  reserved 


OOPYBIGHT,   1915, 

By  the  MACMILLAN  COMPANY. 


Set  up  and  electrotypcd.     Published  July,  1915. 


CAJORf 


J.  S.  Gushing  Co.  —  Berwick  &  Smith  Co. 
Norwood,  Mass.,  U.S.A. 


PREFACE 

As  in  the  Primary  Arithmetic,  so  in  this  Inter- 
mediate Arithmetic,  the  aim  is  to  render  the  sub- 
ject attractive  to  the  pupil,  without  sacrifice  of 
serious  intent.  The  pupil's  self -activity  is  encour- 
aged. By  the  selection,  so  far  as  possible,  of  prob- 
lems bearing  on  the  practical  life  of  to-day,  the 
pupil  is  made  to  feel  that  he  is  engaged  in  studies 
that  are  truly  worth  his  while. 

Our  constant  aim  has  been  to  lay  emphasis  upon 
fundamental  operations.  Frequent  reviews  enable 
the  pupil  to  hold  in  mind  the  new  knowledge  he 
has  acquired. 

As  in  the  Primary  Arithmetic,  so  here,  the  tech- 
nique of  arithmetic  is  simplified,  with  the  aim  of 
securing  greater  economy  of  effort.  Thus  the  sub- 
ject of  ratio  is  robbed  of  some  of  its  terrors  by  its 
identification  with  a  "common  fraction."  A  pro- 
portion expresses  the  "equality  of  two  common 
fractions."  There  is  no  need  of  the  terms  "  ante- 
cedent"  and  "  consequent."  Again,  there  is  given, 
as  an  alternative,  a  simplified  method  of  reading 
decimal  fractions.  After  the  theory  of  decimal 
fractions  is  understood,  .425  is  read  "  Point,  four, 


Q^^^PfH.^ 


Vi  PREFACE 

two,  five."  It  is  recognized  as  a  great  convenience 
to  omit  the  denominator  in  writing  decimal  frac- 
tions ;  why  not  enjoy  the  same  convenience  in 
reading  decimal  fractions  ? 

The  author  takes  pleasure  in  acknowledging  the 
help  he  has  received  in  the  preparation  of  this 
series  of  texts  from  several  teachers  in  the  public 
schools  of  Colorado  Springs,  particularly  from  Mrs. 
L.  D.  Coffin,  Mrs.  S.  J.  Lewis,  Miss  Minnie  L. 
McCall,  and  Miss  Edna  Kinder. 

FLORIAN   CAJORI. 


CONTENTS 
PART  I 

PAOB 

Notation  and  Numeration 1 

Review 1 

Fundamental  Operations 6 

Review 6 

Properties  of  Numbers 29 

Cancellation 34 

Common  Fractions 37 

Review 87 

Quantity  and  Cost 99 

Decimals 109 

Review      .        .        . 132 

Denominate  Numbers 140 

Analysis  and  Solution  of  Problems       ....  172 

Approximations 181 

Averages 183 

Direct  Method  of  Solution 186 

Problems  Illustrated  by  Graphs 189 

PART   II 

Percentage IW 

Application  of  Percentage 214 

Interest =        •  224 

vii 


viii  CONTENTS 

PAGE 

Bills  and  Checks          ....        =        ...  233 

Problems  on  Industry 237 

Review 250 

Positive  and  Negative  Numbers 253 

General  Review 283 

Tables 297 

Tests 298 


INTERMEDIATE   BOOK 


•     •        •      5 


INTERMEDIATE  BOOK 

PART   ONE 

NOTATION  AND  NUMERATION 

Review  —  Oral 

1.  1.  Eead  the  following  numbers : 

125  3,604  40,587  987,500 

360  1,234  18,356  198,799 

405  1,034  97,876  897,747 

987  1,204  99,999  534,689 

2.  Tell  how  many  units  there  are  in  units'  place, 
in  tens'  place,  in  hundreds'  place,  in  thousands' 
place,  in  ten-thousands'  place,  in  hundred-thou- 
sands' place,  in  each  of  the  numbers  in  this  exercise. 

Written  Exercise 
2.   Write  as  one  number : 


10  +  7 

200  +  40  +  5 

3000  +  200  +  50  +  8 

20  +  8 

300  +  60  +  7 

4000  +  500  +  60  +  7 

30  +  9 

400  +  90  +  0 

7000  +  600  +  50  +  4 

40  +  6 

700  +  00  +  8 

8000  +  900  +  10  +  0 

70  +  7 

100  +  10  +  1 

9000  +  000  +  90  +  9 

2':;  '"'. 


INTERMEDIATE  BOOK 


r.f Written  Exercise 


3.   1.    Make  a  number  chart  like  the  illustration. 

Orders  of  Whole  Numbers  Orders  of  Decimals 

Millions  Thousands  Units  or  Ones  Thousandths 


to 

c 
o 

1 

■a 
c 

3 

X 

M 

C 

o 

1 

k 

C 

i 

(0 

■a 
c 

CJ 

u> 

3 

o 

JZ 

*-» 

■6 

0) 

i- 

■a 

E 
3 
I 

C 

ti 

CO 

3 

E 

■M 

c 

1- 

«0 

£ 

m 
to 

3 

o 

to 

1 

T3 
C 
3 

I 

to 

c 

0) 

«o 

o 

c 

o 

1- 

o 
to 

'E 
D 

to 

s: 
•*■> 
c 

to 

s: 
■*-> 
n 

•a 

c 

3 
1 

to 

x: 

■M 

T3 

C 
(« 

to 

3 
O 

JZ 

\- 

3d  Period 

2d  Period 

1st  Period 

1st  Period 

Oral  Exercise 
Based  on  the  Number  Chart 

4.  What  place  is  always  occupied  : 

1.  By  the  figure  that  stands  for  ones? 

2.  By  the  figure  that  stands  for  tens  ? 

3.  By  the  figure  that  stands  for  thousands  ? 

4.  By  the  figure  that  stands  for  hundred-thou- 
sands? 

5.  By  the  figure  that  stands  for  hundreds  ? 


NOTATION  AND  NUMERATION  3 

6.  By  the  figure  that  stands  for  millions  ? 
Name : 

7.  The  order  of  whole  numbers. 

8.  The  order  of  decimals. 

Oral  Exercise 

5.   1.   How  many  ones  make  1  ten  ? 

2.  How  many  tens  make  1  hundred  ? 

3.  How  many  hundreds  make  1  thousand  ? 

4.  How  many  times  greater  is  each  one  than  the 
one  in  the  next  place  or  order  to  the  right  ? 

5.  How  many  times  greater  is  one  of  thousands* 
order  than  one  of  tens'  order  ? 

6.  How  many  times  greater  is  one  in  millions' 
place  than  one  in  thousands'  place  ? 

7.  How  many  times  greater  is  one  in  ten-thou- 
sands' place  than  one  in  hundreds'  place  ? 

8.  How  many  ones  of  the  thousands'  order  are 
equal  to  one  of  the  hundred-thousands'  order? 

Since  each  number  is  ten  times  greater  than  the 
next  unit  to  the  right,  the  system  of  writing  num- 
bers is  called  the  decimal  system.  The  word  deci- 
mal comes  from  the  Latin  word  meaning  ten. 

It  is  easier  to  read  numbers  if  a  comma  is  placed 
between  the  orders  of  hundreds  and  thousands  and 
the  orders  of  hundred-thousands  and  millions. 


4  INTERMEDIATE  BOOK 

Oral  Exercise 

6.  Separate  the   following   numbers  into   their 
orders  and  read  the  numbers : 

1.   4,327 

Process  and  Explanation 

4,327  =  4  thousands  +  3  hundreds  +  2  tens  -f  7  ones 

=  4000  +300  +20       +7 

2.  125           3.  360  4.  405  5.  987 

6.  542            7.  1,234  8.  4,034  9.  7,204 

10.  9,560       11.  5,610  12.  18,356  i3.  78,347 

14.  92,701     15.  72,079  le.  40,679  i7.  198,765 

18.  819,675  19.  576,198  20.  918,567  21.  765,951 

Written  Exercise 

7.  Write  as  one  number  : 

10  +  7  200  +  40  +  5  3,000  +  1,600  +  300  +  50  +  8 
90  +  8  100  +  90  +  6  40,000  +  5,000  +  700  +  90+4 
60  +  9    300  +  63  +  4    30,000  +  6,000  +  200  +  70  +  5 

Written  Exercise 

8.  Fill   in   the   missing   orders   and    write    the 
numbers : 

1.    2  hundreds  +  5  ones. 

Process  and  Explanation 
2  hundreds  +  5  ones  =  2  hundreds  +  0  tens  +  5  ones 
=  205 


NOTATION  AND  NUMERATION  5 

2.  2  ten-thousands  -f  7  thousands  +  6  hundreds  -f- 
7  ones. 

3.  3  hundred-thousands -h  9  hundreds. 

4.  5  millions  +  6  hundred-thousands  -h  4  ten- 
thousands. 

5.  3  hundred-millions  H-  2   ten-millions  H-  5  mil- 
lions +  5  tens. 

6.  1  million +  4  ten-thousands. 

7.  6  ten-millions  +  5  hundred-thousands  -f-  one. 

8.  4  hundred-millions  -h  5  ten-thousands  -h  6  tens 
-f  one. 

Oral  Exercise 

9.  Read  the  following  numbers  : 

7,123                 10,000  673,854 

4,275                 67,431  705,239 

7,155                 10,500  900,432 

1,279                  30,006  821,006 

10,000,000  9,234,567 

For  what  does  0  stand  in  each  of  these  numbers? 


REVIEW   OF   FUNDAMENTAL    OPERATIONS 
Addition 

Oral  Exercise 

10.  1.   Beginning  with  8,  add  by  8  to  96. 

2.  Beginning  with  2,  add  by  7  to  100. 

3.  Beginning  with  1,  add  by  9  to  100. 

4.  Beginning  with  101,  add  by  6  to  200. 

5.  Beginning  with  0,  add  by  5  to  100. 

6.  Beginning  with  0,  1,  2,  3,  4,  5,  add  by  6 
to  100. 

7.  Beginning  with  0,  1,  2,  3,  4,  5,  6,  add  by  7 
to  100. 

8.  Beginning  with  0,  1,  2,  3,  4,  5,  6,  7,  add  by 
8  to  100. 

9.  Beginning  with  0,  1,  2,  3,  4,  5,  6,  7,  8,  add 
by  9  to  100. 

Drill  on  Difficult  Combinations 

11.  Extend  each  set  of  operations  and  drill : 

1.    7       7       7     etc.  2.   8       8       8     etc. 

8     18     28  §     1?     ?^ 

3.    9       9       9     etc.  4.    7       7       7     etc. 

8     18     28  1     ]1     ^ 

6 


REVIEW  OP  FUNDAMENTAL  OPERATIONS   7 

5.  8   8   8  etc.      6.  9   9   9  etc. 
9  19  29  7  17  27 


7.  7  17  27  etc.      8.  7  17  27  etc. 

7   7   7  8   8   8 


9.  7  17  27  etc.     lo.  8  18  28  etc. 

9   9   9  7   7   7 


11.  8  18  28  etc.     12.  8  18  28  etc. 

8  J  _8  ^  _9  _9 

13.  9  19  29  etc.     14.  9  19  29  etc. 

7  7  7  8  8  8 


15.  9  1  29  etc. 

9  9  _9 

12.  Add  rapidly : 

1.  65  2.  67  3.  26   4.  37  5.  48  6.  77 

.  46    43  75     65     59    54 


7.  58  8.  79  9.  46  10.  36  11.  86  12.  74 
47    48    98     67    45   .  75 


8  INTERMEDIATE  BOOK 

Written  Exercise 
13.   Add  and  check  : 

Process 

1.         103  Explanation.  —  The  columns  may 

9  737  he  added  separately   and   the   results 

^gg  added  to  find  the  sum.    In  this  process 

o  ot\A  there  is  no  carrying.     The  process  is 

'      p,  somewhat  simpler  if  sums  of  ten  are 

— ? grouped   together.     3  and  7  make  a 

"^^  group    of   ten.      Indicate    the    other 

1*^  groups  of  ten  in  these  examples.     In 

21  adding  the  first  column  of  Ex.  1,  say : 

17  five,  fifteen,  twenty-five. 
1 


29,255 

2.   317  3.  875   4.  9,762   5.  2,769 

943  465  4,348      8,441 

862  878  7,489     4,798 

198  760  4,765      7,452 

94,628  432  3,484      3,000 

6.  $  13.49  7.  9,876  ft.  8.  3,075  1b. 

3.71  987  64,072 

90.76  7,654  985 
87.33  1,063  70,308 

108.74  9,616  7,293 

98.77  1,007  2,187 

In  adding  dollars  and  cents,  place  the  decimal 
points  under  each  other. 


REVIEW  OF  FUNDAMENTAL  OPERATIONS       9 

Written  Exercise 

14.  Copy  and  add  : 

1.  $475.83 +$437.75 +$789.85. 

2.  $1,198.95 +$364.20 +  $375.98. 

3.  $754 +$7,689.50 +$5,000. 

4.  $376.95 +  $1,234.25 +  $1,990.05. 

Written  Exercise 

15.  Add  by  columns  and  by  lines  : 

1.   9,234  +  8,920+    356  +  9,076  = 

8,456  +  7,122  +  3,738  +  5,951  = 

7,078  +  6,324+    394  +  5,230  = 

■    6,910  +  6,256-1-    404  +  4,545  = 


+  + 


16,263  +  9,790  +  9,920  + 11,002  = 
7,465  +  8,610  +  8,934+  9,003  = 
7,067+  828  +  6,945+  8,004  = 
6,869  +  7,485  +  5,967+   7,112  = 


+  +  +  = 

3.    $40.12 +  $57.28  +  $   4.23 +$35.60 

33.14+    32.93+      4.45+    25.78 

15.16+    21.32+    46.47+    15.96 

7.18+      3.34+      4.89+      6.01 

+  +  + 


10  INTERMEDIATE  BOOK 


4.    $50.71  + $58.74 +$49.89 +  $43.14  = 

47.23  + 

38.88  + 

19.90  + 

34.15  = 

17.45  + 

18.90  + 

8.90  + 

16.17  = 

7.68  + 

9.01  + 

+ 

6.01  + 

+ 

10.19  = 

+ 

= 

Subtraction 

16.  1.    Beginning  with  50,  subtract  by  2  to  0. 

2.  Beginning  with  41,  subtract  by  2  to  1. 

3.  Beginning  with  60,  subtract  by  3  to  0. 

4.  Beginning  with  71,  subtract  by  3  to  2. 

5.  Beginning  with  80,  subtract  by  4  to  0. 

6.  Beginning  with  81,  subtract  by  4  to  1. 

7.  Beginning  with  83,  subtract  by  4  to  2. 

8.  Beginning  with  90,  subtract  by  5  to  0. 

9.  Beginning  with  96,  subtract  by  5  to  1. 
10.    Beginning  with  94,  subtract  by  5  to  4. 

Continue  the  exercise. 

Drill  on  Difficult  Combinations 

17.  Drill  until  habits  of  accuracy  and  rapidity 
are  established. 

1.    17  27  37  47  57  etc. 

7  7  7  7  7 


REVIEW  OF  FUNDAMENTAL  OPERATIONS      11 

2.  17            27            37  47            57  etc. 

_8            _8             ^  J            _8 

3.  17            27            37  47            57  etc. 
_9            _9             _9  _9            _9 

Do  likewise  with  18  and  7,  19  and  7,  18  and 
8,  19  and  8,  19  and  9. 

18.    Subtract  rapidly : 


1. 

67 

2. 

60 

3. 

75 

4. 

92 

5. 

80 

25 

28 

46 

43 

34 

6. 

55 

7. 

45 

8. 

99 

o. 

91 

10. 

83 

27 

32 

35 

57 

45 

11. 

74 

12. 

95 

13. 

52 

14. 

73 

15. 

45 

32 

26 

23 

24 

39 

Written  Exercise 
19.   Subtract  and  check  : 

p  Ij /~v  pt  "pi  ca  Q 

.^  -or  Explanation.    4  and  1  are  5; 

1.  4U,7d&      g  ^^^  y  ^^.^  ^3 .  ^  ,^^^  2  ^j  ^j^^  j^ 

^^^^^^      are  7  ;  9  and  1  are  10. 
1,171  Ans. 

2.  107,864    3.  987,603     4.  367,890 

72,895      367,809       176,805 

5.  134,578    6.  3,764,001   7.  500,897,431 
90,387      1,987,373      176,354,897 


12  INTERMEDIATE  BOOK 

8.  $754.37        9.    $7,689.50      lo.   $7,989.50 
376.95  1,234.25  1,990.35 

Written  Problems 

20.  1.  A  man  had  $  1,000  in  a  bank.  He  drew 
out  the  following  amounts:  $95.50,  $180.65, 
$75.05,  $96.75,  $7.85,  $1.25,  $60.73. 

How  much  money  remained  in  the  bank  ? 

2.  A  man  earned  $  30.45  in  January,  $  40.26  in 
February,  $42.19  in  March,  $61.34  in  April, 
$53.50  in  May,  $39.29  in  June,  $27.00  in  July, 
$47.45  in  August,  $40.10  in  September,  $  50.24  in 
October,  $  55.75  in  November.  During  the  month 
of  December  he  was  idle.  If  his  expenses  during 
the  year  were  $  240,  how  much  did  he  save  ? 

3.  The  Panama  Canal  is  about  50.4  mi.  long. 
The  first  8  mi.  are  a  sea-level  channel.  The  next 
24  mi.  are  through  a  lake  above  sea  level.  From 
this  point  the  channel  passes  7^  mi.  through  a  cut  in 
the  Culebra  Hill.  The  channel  then  passes  through 
a  lake  5  mi.  long.  The  rest  of  the  distance  is  a 
sea-level  channel.  How  long  is  the  last  section  of 
the  canal  ? 

4.  The  aggregate  population  of  25  cities  of  the 
United  States  in  1910  was  11,042,500.  In  1900 
they  had  an  aggregate  population  of  8,273,482 ;  in 
1890  they  had  6,213,583.     What  was  the  increase 


REVIEW  OF  FUNDAMENTAL  OPERATIONS     13 

in  population  from  1890  to  1900  ?  What  was  the 
increase  in  population  from  1900  to  1910  ?  How 
does  the  increase  between  1890  and  1900  compare 
with  the  increase  between  1900  and  1910?  Which 
is  the  greater  ?     How  much  greater  is  it? 


Multiplication 

Okal  Drill 

21.   How  much  is 

1.   7x8         2.     6x9  3.  9x7 

5.   9x4         6.     9x6  7.  7x9 

9.    6x12     10.  12x7  11.  12x9 

13,     7x11       14.    11x8       15.      9x11 


4.  8x8 

8.  8x7 

12.  8x12 

16.  11x6 


Oral  Exercise 

22.   Multiply  the  numbers  in  the  upper  line  by 
each  number  in  the  lower  line : 


3 

7 

6 

5 

2 

4 

11 

8 

12 

10 

9 

X 

4 

7 

9 

3 

12 

6 

5 

11 

8 

2 

3 

7 

6 

5 

2 

4 

11 

8 

12 

10 

9 

X 

10 

100 

1000 

Make  devices  that  provide  drill  upon  the  prod- 
ucts in  which  you  fail. 


14 


INTERMEDIATE  BOOK 


Drill  — Magic  Circle 

23.  1.  If  the  8  vacant  spaces  are  properly  filled, 
we  get  circles,  called  "  magic  circles."  Lines  radi- 
ating from  the 
center  divide 
the  circles  into 
8  parts.  Fill 
the  empty 
spaces  so  that 
the  sum  of  all 
8  numbers  in 
4c/  each  part,  plus 
the  number  in 
the  middle,  is 
360. 

2.    If    the 

empty  spaces  are  properly  filled,  then  the  sum  of 
the  8  numbers  in  any  one  ring,  together  with  the 
number  in  the  middle,  is  360.  Add  and  show 
that  this  is  true. 

3.  Show  that  the  sum  of  the  numbers  in  any 
half  ring,  above  the  line  AB  or  below  it,  together 
with  half  the  middle  number,  is  180. 

4.  Show  that  the  sum  of  any  four  numbers,  each 
next  to  the  other  three,  together  with  half  the 
middle  number,  is  equal  to  180.  Thus,  20,  67,  75, 
12  are  four  such  numbers,  also  14,  25,  72,  63. 


REVIEW  OF  FUNDAMENTAL  OPERATIONS      15 

Written  Exercise 
24.    Find  the  product : 
1.    648 
14 


Process  Explanation.  —  To  multiply  648  by 


648 
14 


14  means  to  multiply  648  b}^  4  and  10. 

The  process  of  multiplying  648  by  4  is  to 

multiply  by  4  ones.  It  remains  to  multi- 
^  ply  648  by  1  ten.     This  gives  648  tens, 

^^^  Since  the  number  is  tens,  the  first  figure, 

9072         8,  is  written  in  tens*  place.     The  vacant 

place  is  sometimes  filled  in  with  a  0.    This 

is  not  necessary. 

4.  295     5.  798 
32        16 


2. 

754 

3. 

423 

24 

36 

6. 

581 

7. 

649 

24 

52 

10. 

953 

11. 

825 

21 

6^ 

14. 

558 

15. 

275 

28 

■  27 

18. 

589 

19. 

643 

76 

87 

22. 

7,245 
58 

23. 

9,398 
69 

8.  959     9.  764 

27        24 


12.  647     13.  939 
68        44 


16.  821     17.  478 
97        84 


20.  824  21.  7,468 

48      47 

24.  8,556  25.  5,729 
76       87 


16  INTERMEDIATE  BOOK 

26.  5,749   27.  3,128   28.  1,847   29.  3,985 
89     96       97      98 

30.  9,346   31.  9,098   32.  9,009   33.  9,999 
99     78      89      86 

Written  Problems 

25.  Find  the  cost  of : 

1.  64  gallons  of  oil  at  17  ^  per  gallon. 

2.  47  pounds  of  tea  at  48  ^  a  pound. 

3.  6  dozen  penknives  at  $  8.75  a  dozen. 

4.  25  barrels  of  flour  at  $  4.25  a  barrel. 

5.  50  dozen  eggs  at  27^  a  dozen. 

6.  620  pounds  of  chicken  at  19  ^  a  pound. 

7.  72  packages  of  crackers  at  15  ^  a  package. 

8.  6  firkins  of  butter,  each  containing  100  pounds, 
at  26  ^  a  pound. 

Mxiltiplication  by  more  than  Two  Digits 

26.  Multiply: 

1.   1,854  by  237. 
Process        Explanation.  —  Multiply  by  7  ones. 
1  ftf^l        Write  the  product  so  that  its  right-hand 
'oQ7  ^^^^^  ^^  ^^  ones'  column,  under  the  7. 

Multiply  by  8  tens.     Write  the  product 


12978  so    that    its    right-hand    digit    is    in    tens' 

5562  column. 
3708  Then   multiply   by   2   hundreds.     Write 

i  qq  qqo  the  product  so  that  its  right-hand  digit  is  in 

'  hundreds'*  column.     Add  the  three  products. 


REVIEW  OF  FUNDAMENTAL  OPERATIONS      17 

2.  175  bj  206. 

Process       Explanation.  —  In  this  exercise  it  is  nec- 

-ifrr        essary  to  multiply  by  six  ones  and  two  hun- 

9nA        dred.     Multiplying  by  two  hundred  may  be 

— - —       done  by  multiplying  by  two  and  moving  the 

product  two  places  to  the  left.     The  vacant 

^^^  places  are  shown  under  the  5  and  the  cipher. 

31,550 

3.  312  by  620. 
Process 

312  Explanation.  —  Multiply  first  by   two 

620  tens^  then  by  six  hundreds.     Fill  in  the  first 

5240  place  with  a  cipher.      There   are   no   ones. 

1872  '^^^  ^^^^  partial  product  is  312  times  2  tens. 

193,449 


Written  Exercise 

27. 

Multiply : 

1. 

123  by  123 

2.   497  by  132 

3. 

568  by  231 

4.   759  by  322 

5. 

897  by  432 

6.   575  by  405 

7. 

612  by  740 

8.   1,019  by  305 

9. 

765  by  600 

10.   896  by  500 

11. 

1,324  by  901 

12.   897  by  700 

13. 

678  by  509 

14.   437  by  987 

Division 

28. 

Give  the  answer : 

1. 

56^8       2.  63-^ 

•  9      3.  72-^8      4 

48-4-6 


18 


INTERMEDIATE  BOOK 


5.   54^9       6.  64-^8      7.  63-^7      8.  49-^7 

9.   81-^9     10.  84-4-7     11.  45H-9     12.  55^5 

13.   60-^12   14.  72^12  15.  84-4-12  le.  99-i-ll 


Oral  Exercise 

29.   Divide  each  number  in  the  upper  line  by 
each  number  in  the  lower  line. 


2. 


60 

24 

36 

72 

48 

144 

96 

-^ 

2 

3 

6 

4 

12 

9 

1,000 

10,000 

17,000 

90,000 

-r- 

10 

100 

1,000 

30.   Divide 
1.    43,641 
Process 
614^1 


71)43641 
426 


104 
71 


331 

284 
47 


Division  by  Two  Digits 

by  71. 

Explanation.  —  Indicate  above  the 
dividend  by  a  small  cross  mark,  x,  the 
last  or  right-hand  figure  in  the  first 
partial  dividend. 

436  is  the  first  partial  dividend. 
(Try  436^70.)  436^71  =  6  and  a 
remainder.  Place  the  6  above  the  last 
figure  in  the  partial  dividend.  6  x  71 
=  426  ;  436  -  426  =  10,  the  remainder. 
Bring  down  the  4,  the  next  figure  in  the 
dividend.      104   is   the   second   partial 


REVIEW  OF  FUNDAMENTAL  OPERATIONS      19 

dividend.  (Try  104 -- 70.)  104^71  =  1  and  a  remain- 
der. 1  X  71  =  71 ;  104  -  71  =  33,  the  remainder.  Bring 
down  the  1,  the  next  figure  in  the  dividend.  (Try 
331^70.)  331^71  =  4  and  a  remainder.  4x71  =  284; 
331  -  284  =  27,  the  last  remainder. 

The  quotient  is  614  and  the  remainder  47,  or  614|^. 

Ans, 

2.  $  158.22  by  54. 

Process  Explanation. — The    first    partial 

$  2  93  dividend  is  158.     Trial  division   indi- 

^ Gates   that   54   is  contained   in  153,  3 

54)$  158.22  ^ij^gg^     3x54  =  162.     162    is   greater 

IQ^  than  the  first  partial  dividend.    1 58  -^  54 

502  =  2   and   50    remainder.     The    second 

486  partial  dividend  is  502.     502-^54=9 

162  ^^^  16  remainder.     The  third  partial 

252  dividend  is  162.     162  --  54  =  3. 

$2.93  Ans. 

3.  2,790  by  29. 

Process 

96^         Explanation. — 279  is  the  first  par- 

9QT97^  tial  dividend.     Use  30  for  trial  divisor. 

^9)^790  279-^30  =  9.     9x29  =  261;    279-261 

"^^^  =18  remainder.     The  next  partial  divi- 

180  dend  is  180.  180  -^  30  =  6.  6  x  29  =  174  ; 

174  180  -  174  =  6  remainder.     96/^  Ans. 

6 

When  the  ones'  figure  is  9,  as  29,  39,  etc.,  it  is 
generally  easier  to  use  30,  40,  etc.,  as  a  trial 
divisor. 


20  INTERMEDIATE  BOOK 

Written  Exercise 

31.  Divide : 

1.  4,875  by  31  2.  2,849  by  42 

3.  18,785  by  23  4.  54,632  by  77 

5.  64,751  by  78  6.  60,543  by  89 

7.  49,790  by  96  s.  38,000  by  67 

9.  50,000  by  65  lo.  $  657.50  by  24 

11.  $  785.60  by  26  12.  $  6000.00  by  33 

Division  by  more  than  Two  Digits 

32.  Divide : 

1.  6,084  by  234. 

Process  Explanation.  —  234  is  contained  in 

26  608,  2  times,  and  a  remainder. 

1_  Write  the  2  of  the  quotient. 

234)6084  234  into  1404  goes  6  times. 

468  Write  the  6  of  the  quotient.     There 

1404  is  no  remainder. 

1404  The  answer  is  26. 

2.  8,499  by  293. 

Process  Explanation.  —  Since  293  is  nearly 

29  300,  it  is  convenient  to  use  300  as  our 

^  trial  divisor  to  find  the  first  figure  in 

293)8499  the  quotient. 

586  300  is  contained  in  849,  2  times. 

2639  Write  the  2  of  the  quotient  over  the  9, 

2537  the  last  figure  of  the  partial  dividend,  849. 

2  ^^^  ^^^^  2639  goes  nearly  9  times. 
Try  9. 


REVIEW  OF  FUNDAMENTAL  OPERATIONS     21 

293  X  9  is  less  than  2639.     Hence  9  is  the  second 
figure  of  the  quotient. 

The  quotient  is  29,  the  remainder  is  2. 


Written  Exercise 

33. 

Divide  and  check : 

1. 

19,623  by  211 

2. 

17,347  by  209 

3. 

40,260  by  915 

4. 

52,288  by  817 

5. 

15,022  by  406 

6. 

33,744  by  703 

7. 

20,262  by  614 

8. 

16,302  by  429. 

9. 

37,700  by  725 

10. 

50,255  by  529. 

11. 

19,277  by  663 

12. 

28,644  by  682 

13. 

20,000  by  607 

14. 

50,000  by  600 

15. 

60,000  by  705 

16. 

75,000  by  850 

Divisors  10,  20,  100,  600 
34.   Divide: 

1.  87  by  10. 

Process         Explanation.  —  87  =  8  tens  +  7  ones. 

^ro         10  is  contained  in  8  tens  +  7  ones  8  times 

lj9)8|7       with  7  as  a  remainder  or  S^. 

A  short  method  of  dividing  a  number  by  10  (when 

the  dividend  does  not  end  with  a  0)  is  to  separate  the 

tens  from  the  ones  by  a  vertical  line  and  divide. 

2.  7,300  by  100. 

Process  Explanation.  —  7,300  =  73  hundreds. 

H-o  1  hundred  is  contained  in  73  hundreds 

mWm      'VsTL  quotient. 


22  INTERMEDIATE  BOOK 

A  short  method  of  dividing  by  100  a  number  that 
ends  with  two  O's  is  to  cancel  the  two  O's  at  the  right 
of  the  divisor  and  the  dividend,  and  divide. 

2.  3,660  by  200. 

Process  Explanation.  —  Write    the    explana- 

18-^     tion. 
200)36|6O         Explain  a  short  method. 

3.  4,575  by  300. 

Process  Explanation.  —  Write    the   explana- 

15^      tion. 
300)45175  Canceling  a   cipher  at  the    right  of  a 

number  divides  the  number  by  what  ? 
Canceling   two   ciphers  at   the   right  of   a  number 
divides  the  number  by  what? 


Written  Exercise 


35.    Divide : 


1.     30)127  2.  40)4,326 


4.     60)4,563       5.  70)7,564 


7.  90)9,046         8.  30)2,147 


10.  80)3,064        11.  90)6,847 


13.  100)8,400      14.  200)7,800 


16.  500)64,500    17.  600)9,600 


19.  800)89,700    20.  900)54,600 


3. 

50)6,534 

6. 

80)6,574 

9. 

40)8,435 

12. 

70)9,037 

15. 

400)97,600 

18. 

700)8,890 

21. 

600)93,310 

22.  700)33,970    23.  800)828,240    24.  900)565,830 


REVIEW  OF  FUNDAMENTAL  OPERATIONS      23 

Oral  Problems 

36.  1.   What  is  the  cost  of  20  lb.  of  beef  at  23^ 
a  pound  ? 

2.  A  clerk  in  a  store  sold  30  sets  of  books  at 
$  6  per  set.     How  much  did  he  receive  altogether? 

3.  How  far  will  a  train  travel  in  12  hours  at 
the  rate  of  40  miles  an  hour  ? 

4.  At  4  miles  per  hour,  how  long  will  it  take  a 
man  to  walk  52  miles  ? 

5.  How  many  inches  are  there  in  30  feet  ?     In 
40  feet? 

6.  How  many  feet  are  there  in  240  inches  ? 

7.  At  6^  a  quart,  how  many  quarts  of  milk  can 
be  bought  for  78^?  90^? 

8.  What  is  the  cost  of  eggs  a  dozen,  if  7  dozen 
cost  $2.80? 

9.  What  is  the  cost  of  9  dozen  eggs  at  40^  a 
dozen  ? 

10.    How  many  square  feet  in  288  sq.  in.? 

Written  Problems 

37.  1.    Find  the  number  of  minutes  in  24  hours. 

2.  How  many  hours  in  the  month  of  July  ? 

3.  Find  the  number  of  hours  in  365  days. 

4.  How  many  feet  in  76  miles  ?   1  mi.  =  5280  ft. 


24  INTERMEDIATE  BOOK 

5.  What  is  the  weight  in  pounds  of  15|-  tons  of 
coal  ?  1  T.  =  2000  lb. 

6.  How  many  street  cars  are  necessary  to  carry 
901  passengers,  if  53  passengers  are  put  into  each 
car? 

7.  A  train  runs  984  miles  in  24  hours.  How 
many  miles  does  it  run  an  hour  ? 

8.  On  a  city  street  there  are  139  houses.  Each 
house  contains  4  families  and  each  family  6  persons. 
How  many  persons  live  on  the  street  ? 

9.  A  booklet  has  65  pages.  There  are  30  lines 
on  each  page  and  in  each  line  43  letters.  How 
many  letters  are  there  in  the  book? 

10.  4,368  oranges  are  to  be  packed  in  56  boxes 
of  equal  size.  How  many  oranges  must  be  put 
into  each  box? 

11.  What  number  multiplied  by  73  will  give 
4,526? 

12.  How  many  bushels  of  potatoes  will  54  acres 
yield,  if  each  acre  yields  243  bushels? 

13.  35  acres  yield  8,295  bushels  of  potatoes. 
How  many  bushels  is  this  per  acre? 

14.  It  is  85  miles  from  Chicago  to  Milwaukee. 
How  many  rods  is  this? 

15.  From  New  York  to  Buffalo  it  is  411  miles. 
How  many  miles  does  a  man  travel  in  going  18 
times  from  one  city  to  the  other? 


REVIEW  OF  FUNDAMENTAL  OPERATIONS     25 

16.  A  locomotive  has  been  run  75  times  between 
Chicago  and  New  York.  The  distance  between 
these  cities  is  908  miles.  How  many  miles  has 
this  locomotive  traveled? 

17.  If  29  acres  of  land  cost  $  3,828,  what  is  the 
cost  of  1  acre? 

18.  If  an  automobile  travels  23  miles  an  hour, 
how  far  will  it  go  in  78  hours? 

19.  At  27  miles  an  hour,  how  long  will  it  take 
an  automobile  to  go  351  miles? 

20.  At  57^  a  bushel,  what  is  the  cost  of  125 
bushels  of  potatoes? 

21.  The  President  of  the  United  States  has  a 
salary  of  $  75,000  per  year.  How  much  does  he 
receive  per  month?  Per  day,  counting  365  days 
to  the  year? 

22.  A  man  started  on  a  journey  of  620  miles. 
After  he  had  traveled  15  hours  at  the  rate  of  39 
miles  an  hour,  how  far  was  he  from  his  journey's 
end? 

23.  How  many  pounds  of  coffee,  at  60^  a  pound, 
will  cost  as  much  as  120  gallons  of  molasses  at 
57^  a  gallon? 

24.  A  merchant  makes  five  payments  of  $  1,275 
each  on  a  debt  and  finds  that  he  still  owes  $  785. 
How  much  was  the  debt? 


26 


INTERMEDIATE  BOOK 


25.  A  store  has  475  boxes  of  soap,  each  box 
containing  175  cakes.  What  is  the  entire  number 
of  cakes? 

26.  A  factory  made  2,748  suits  during  a  season. 
At  $  19  a  suit,  how  much,  was  received  for  them? 

27.  A  man  sold  a  farm  for  $  5,775  and  gained 
$1,200.  What  would  have  been  the  selling  price 
if  he  had  gained  $  1,354? 

28.  If  525  gallons  of  milk  sell  for  $  84,  what  is 
the  rate  per  gallon? 

Oral  Exercise 
38.   1.     Let  the  drawing  represent  1  sq.  yd. 

2.  Then  the 
9  smaller  divi- 
sions represent 
what? 

3.  How  many 
square  feet  in 
1  sq.  yd.? 

4.  What  does 
each  small  di- 
vision in  A  rep- 
resent? 

5.  How  many  small  squares  in  one  row  in  ^? 

6.  How  many  rows  of  small  squares  in  A  are 
there? 


:::::j5::::ii 


REVIEW  OF  FUNDAMENTAL  OPERATIONS      27 

7.  How  many  small  squares  in  J.? 

8.  Make  the  table  of  square  measure. 

Construction  Exercise 

39.  1.  Draw  a  square,  one  inch  long  and  one 
inch  wide.     Call  it  a  square  inch. 

2.  Draw  a  rectangle  4  in.  long  and  2  in.  wide. 
The  picture  shows  the  rectangle  smaller  than  it 
really  is.  How  many  square 
inches  are  there  in  one  row?  In 
the  two  rows?  What  is  the  area 
of  the  rectangle?  Tell  how  to 
find  the  area  of  a  rectangle. 

3.  How  many  square  inches  are  there  in  a  square 
that  is  12  in.  long  and  12  in.  wide?  How  many 
square  inches  make  a  square  foot? 

4.  How  many  square  feet  are  there  in  a  square, 
3  feet  long  and  3  feet  wide  ?  How  many  square 
feet  make  a  square  yard? 

The  area  of  a  rectangle  is  ohtained  hy  multiplying 
its  length  hy  its  width. 

Written  Exercise 

40.  1.    How  many  square  feet  in  139  sq.  yd.? 

2.  How  many  square  inches  in  15  sq.  ft.? 

3.  How  many  square  yards  in  1  sq.  mi.? 

4.  How  many  square  yards  in  180  sq.  mi.? 

5.  How  many  feet  in  108  mi.? 


28  INTERMEDIATE  BOOK 

Written  Problems 

41.  1.  Find  the  area  of  a  floor,  the  dimensions 
of  which  are  6  yd.  by  5  yd. 

2.  Find  the  number  of  square  yards  in  the  sur- 
face of  a  wall  9  ft.  high  and  15  ft.  long. 

3.  A  garden  is  48  ft.  by  120  ft.  There  is  a 
gravel  walk  3  ft.  wide  around  the  outside  of  the 
garden.  Make  a  drawing  of  the  garden  (scale, 
1  in.  =  1  ft.)  and  show  the  walk. 

4.  What  is  the  area  of  the  garden  in  square 
feet? 

5.  What  is  the  area  of  the  walk  in  square  feet? 

6.  What  is  the  area  of  the  garden  and  walk? 

7.  A  piece  of  land,  16  rd.  long  and  10  rd.  wide, 
is  divided  into  4  equal  parts  by  lines  4  rd.  apart. 
What  are  the  dimensions  of  each  part? 

8.  How  many  square  rods  in  each  part  ? 


PROPERTIES    OF   NUMBERS 
Factors 

42.  A  factor  of  a  whole  number  is  an  integer 
that  is  an  exact  divisor  of  that  number. 

Thus,  the  number  24  has,  besides  itself  and  1, 
the  factors  2,  3,  4,  6,  8,  12. 

A  prime  number  is  an  integer  that  has  no  fac- 
tors, except  itself  and  1. 

2,  3,  7  are  examples  of  prime  numbers.  It  is 
evident  that  7  is  not  exactly  divisible  by  any  integer, 
except  itself  and  1.  Hence  it  is  a  prime  number. 
The  same  is  true  of  2  and  3. 

A  prime  factor  is  a  factor  that  is  a  prime  number. 

2  and  3  are  prime  factors  of  24. 

Oral  Exercise 

43.  1.   Is  8  a  prime  number?     Why? 

2.  Is  11  a  prime  number?     Why? 

3.  There  are  4  prime  numbers  between  1  and 
10.     Find  them. 

4.  There  are  4  prime  numbers  between  10  and 
20.  Find  them. 

5.  Find  the  prime  numbers  between  20  and  30. 

6.  Name  the  prime  factors  of  4,  6,  8,  9,  10,  12. 

29 


30  INTERMEDIATE   BOOK 

Divisibility  of  Numbers 

44.  A  whole  number  is  exactly  divisible  by  2,  if 
the  digit  in  ones'  place  is  2,  4,  6,  8,  or  0. 

A  whole  number  is  exactly  divisible  by  5,  if  it 
ends  in  5  or  0. 

A  whole  number  is  exactly  divisible  by  3,  if  the 
sum  of  its  digits  is  divisible  by  3. 

For  example,  432  is  exactly  divisible  by  3, 
because  the  sum  of  its  digits  (4  +  3  +  2)  is  9,  and  9 
is  exactly  divisible  by  3. 

A  whole  number  is  exactly  divisible  by  6,  if  it  is 
even  and  exactly  divisible  by  3. 

Thus,  168  is  even;  1  +  6  +  8  =  15;  hence  168  is 
exactly  divisible  by  6. 

A  whole  number  is  exactly  divisible  by  4,  if  the 
number  made  up  of  the  two  right-hand  digits  is  so 
divisible.  Thus,  3148  is  exactly  divisible  by  4, 
because  48  is  so  divisible. 

A  whole  number  is  exactly  divisible  by  8,  if  the 
number  made  up  of  the  three  right-hand  digits  is 
so  divisible.  Thus,  94,128  is  exactly  divisible  by  8, 
because  128  is  so  divisible. 

Oral  Exercise 

45.  1.  What  numbers  multiplied  together  give 
the  following  products : 

33         16         26         27         32         30         34 
35         36         42         44         45         48         49 


PROPERTIES  OF   NUMBERS  31 

2.  What  whole  numbers  will  exactly  divide: 

44    46    63    64    54     56 

72    81    84    88    96    108 

3.  Name  two  factors  of  12. 

P  HOC  ESS 

1 9  _  Q      A  Explanation.  — 3  and  4  are  called 

factors  of  12. 

^^  2  and  6  are  also  factors  of  12. 

2x6 

4.  Name  two  factors  of  each  of  the  following: 

65    35    42    50    72    48 
24    18    36    45    33    27 


Oral  Exercise 
46.   1.    Name  two  factors  of  each  of  the  follow- 


ing: 

6 

10 

15 

21 

26 

33 

35 

39 

49 

55 

25 

22 

2.  Name  three  factors  of  each  of  the  following: 

8         12         16         18         24        27 
30         36         42         45         48         54 

3.  Name  all  the  factors  of  each  of  the  following; 

33    56    64    49     72     81 
63    54    96    108    120    144 


32  INTERMEDIATE  BOOK 

4.  Which  of  the  following  numbers  are  exactly 
divisible  by  2?  By  3?  By  4?  By  5?  By  6? 
By  8? 

15,  18,  24,  30,  42,  45,  48,  62,  170,  212,  312, 
330,  450,  790,  1,012,  3,618,  7,544,  6,908,  4,345, 
7,545,  10,000. 

5.  The  prime  factors  of  12  are  2,  2,  and  3. 
What  are  the  prime  factors  of  15?   Of  18?   Of  24? 

6.  Name  the  prime  factors  of  14;  of  28;  of  30; 
of  42;  of  45;  of  49;  of  50. 

Finding  Prime  Factors 
47.   1.    Find  the  prime  factors  of  36. 

Process  Explanation.  —  36  is  exactly 

2)36 


divisible  by  2.     Why  ? 


18    is    exactly    divisible    by    2. 

^)_  9  is  exactly  divisible  by  3. 

3)   3  The  prime  factors  of  36  are 

36  =  2x2x3x3.       2x2x3x3. 

2.    Find  the  prime  factors  of  450. 

Process  Explanation.— 10,  9,  5,  and  3  are 

5)450  all  factors  of  540. 

5)90  In   finding   the  prime   factors  it  is 

3)18  better  to  factor  by  the  prime  factors. 

Therefore  divide  450  by  5,  5,  3,  3,  and  2. 


3)_6 
2 
1 


o\~2~  ^^'^^  prime  factors  of  450  are: 

^ "  2x3x8x5x5. 


PROPERTIES  OF  NUMBERS  33 

Written  Exercise 
48.   Find  the  prime  factors  of 

1.  72    75    81 

2.  120    125    128 

3.  201    195    333 

4.  340    570    690 


96 

108 

144 

150 

444 

234 

640 

729 

CANCELATION 

49.   1.    Divide  12  x  15  by  8  x  10. 

Process  by  Cancelation  Explanation. — 

o        o  Take  the  common  fac- 

12  X  15_  ;i^  X  U  (Dividend)  ^^''.^  °"*  °*  ^^  in  the 

"o — T7r~~o — TnT   /t\'   •       \  dividend    and     8    in 

8x10       8x10    (Divisor)  ,,       -,.  .         ,      . 

no  the    divisor,    leaving 


3       3 


the  factors  3  and  2. 
Take  the  common  fac- 


l^^l^  =  ^^^  =  ^=  21  tor  5  out  of  15  in  the 

f>xlp      2x2     4        *  dividend,  and   10   in 

^       ^  the  divisor  leaving  the 

factors  3  and  2.  Find 
the  product  of  3  x  3,  the  remaining  factors  in  the  divi- 
dend, and  2x2,  the  remaining  factors  in  the  divisor 
and  divide. 

•         12  X  15 
2.    Divide,  using  cancelation,  . 

10  X  18 

Explanation.  —  Re- 

Process  3®^^  t^^®  common  factors 

6  and    5  from  both   the 

2       3 

-t%     7 «      a  dividend  and  the  divisor. 

IfAi^  =  MAM  =  5=1  Divide  the  product  of 

10  X  18     ;I0  X  ;i^     6  the   factors  in  the   divi- 

^        *^.  dend  by  the  product  of 

the  factors  in  the  divisor. 

34 


CANCELATION  35 

12  X  15  X  42 

3.    Divide,  usino;  cancelation,  — 

'     8x9x24 

Process  Explanation.  — 

^        w       -|  .  Reject   the    common 

io      -I  ^      ^o      fiji      Ttf      4  0i  factors   4,    3,    and    3 

I     a"\,    -^l^^f^f-      f-»  both   the  divi. 
8x9x24  |X^>^^^  dend  and  the  divisor. 

Reject  the  common 
7  factors  3  and  2  from 

^        5       Jif:  the  new  dividend  and 

jLfXjLpx  ff  _  ^  _.  43.  divisor. 

^  X  ^  X  ;^^         8         ^  Divide  the  product 

^      ^       8  of  the  remaining  fac- 

tors of  the  dividend 
by  the  product  of  the  remaining  factors  of  the  divisor. 


PRINCIPLE   TO  BE  REMEMBERED 

Dividing  both  dividend  and  divisor  by  the 
same  factor  does  not  change  the  value  of  the 
quotient. 


Written  Exercise 
50.   Divide,  using  cancelation : 

1.  24  X  49  X  18  by  12  x  21  x  36 

2.  25  X  35  X  56  by  15  x  28  x  49 

3.  32  X  108  X  100  by  64  x  36  x  25 

4.  39  X  28x72  by  35x52x24 

5.  16x40x24  by  20x8x48 


36  INTERMEDIATE  BOOK 

30  X  32  X  36  X  40  350  x  120  x  72 

^50x16x20x18  '^*     500x63x6 

625x49x81  1728  x  99  x  100 

°*   75x210x140  ^*   1440x108x25 

625x1728x121x1000 


10. 


2500  X  720  X  99  X  24 


f 

7 
8 

1 

U 

1* 

tf 

M* 

f 

¥ 

¥ 

-V- 

w- 

W 

m 

H 

4| 

5| 

9* 

25i 

135j^ 

97ii 

COMMON  FRACTIONS 

Review 

51.   Read  the  fractions.     Which  number  is  the 
numerator  ?     Which  the  denominator  ? 
1. 

2. 

3. 

In  which  of  these  fractions  is  the  numerator  less 
than  the  denominator  ? 

In  which  of  these  fractions  is  the  numerator 
greater  than  the  denominator  ?  One  or  more  of  the 
equal  parts  of  a  unit  is  called  a  fraction. 

The  denominator  shows  into  how  many  equal 
parts  the  unit  is  divided. 

The  numerator  shows  how  many  of  the  equal 
parts  have  been  taken. 

The  numerator  and  denominator  are  sometimes 
called  terms  of  the  fraction. 

A  proper  fraction  is  one  whose  numerator  is  less 
than  its  denominator.     For  example,  ^,  f,  f. 

An  improper  fraction  is  one  whose  numerator  is 
equal  to  or  greater  than  its  denominator.  For 
example,  |,  |,  f . 

A  mixed  number  is  an  integer  and  a  common 
fraction  taken  together.     3f  is  a  mixed  number. 

37 


38  INTERMEDIATE  BOOK 

Oral  Exercise 
52.   Name  the  unit  in  each  of  these  fractions : 

1.  fbu.  I- mi.  1^0  lb.  f  ft. 

2.  f  of  an  apple ;  |  of  a  circle  ;  |  of  a  rectangle. 

3.  Into  how  many  equal  parts  has  each  of  these 
units  been  divided  ? 

4.  What  term  of  the  fraction  shows  into  how 
many  equal  parts  the  unit  has  been  divided  ? 

5.  How  many  equal  parts  of  the  unit  have  been 
taken  in  each  of  these  fractions  ? 

6.  What  term  of  the  fraction  shows  how  many 
of  the  equal  parts  have  been  taken  ? 

7.  f  means  that  1  unit  is  divided  into  6  equal 
parts  and  that  4  parts  are  taken. 

I  may  be  explained  also  as  meaning  6)4.  The 
dividend  being  smaller  than  the  divisor,  we  indicate 
the  division  by  writing  |.     The  simpler  form  is  |. 


53.    1. 


2. 


Drill  Exercise 

100^=  $1 

25^  =  $i 
75^  =  $f 

12  in.  =  1  ft. 
6  in.  =  1  ft. 
3  in.  =  i  ft. 

lin.  =  ii2ft- 
2  in.  =  1  ft. 

8  in.  =  1  ft. 

COMMON  FRACTIONS  ^     39 

3.         16oz.  =  llb.  loz.  =  3iglb. 

8oz.  =  ^lb.  2oz.  =  i-lb. 

4  oz.  =  ilb.  12oz.  =  |lb. 

Oral  Exercise 

54.  1.    What  part  of  a  dollar  is  1  dime  ? 

2.  What  part  of  a  dollar  are  5  dimes  ?  2  dimes  ? 

3.  What  part  of  a  dollar  is  1  nickel?  What 
-part  are  2  nickels  ?  4  nickels  ?  5  nickels  ?  10  nick- 
els? 

4.  What  part  of  a  dollar  are  2  nickels  and  1 
dime? 

5.  What  part  of  a  dollar  are  2  nickels  and  4 
dimes  ? 

6.  What  part  of  a  dollar  are  2  dimes  and  1  nickel  ? 

7.  What  part  of  a  foot  are  3  inches  and  1  inch  ? 

8.  Three  books,  each  1  inch  thick,  are  placed 
upon  a  library  shelf.  What  part  of  a  foot  of  shelf- 
room  do  they  occupy  ? 

Reduction  of  Fractions 

55.  1.    Examine  the  drawing  of  the  ruler. 


3  2  1 


2.  How  many  half  inches  in  one  inch  ? 

3.  How  many  fourths  of  an  inch  in  one  inch  ? 


40 


INTERMEDIATE  BOOK 


4.  How  many  eighths  of  an  inch  does  f  in.  lack 
to  make  1  in.  ? 

5.  How  many  fourths  make  one  half  ? 

6.  Compare  ^  in.  in  length  with  J  in. 

7.  How  many  eighths  in  one  fourth  ? 

8.  Examine  the  draw- 
ing of  the  square. 

9.  How  many  thirds 
of  the  whole  square  are 
shaded  ? 

10.   How    many    ninths 

of   the   whole   square   are 

shaded?     The   illustration 

shows  that  |  =  f. 

11.   Divide  both  terms  of  the  fraction  |  by  3, 


thus:  ?  =  -.     To  divide  both  terms  of  the  fraction 
^     3 

3 

f  by  3,  cancel  the  common  factor  3  and  reduce  f  to 
lower  terms,  f . 

^  is  reduced  to  ^  by  canceling  the  common  factor 
1 

4,  thus:   1=1. 


12.    How  is  I  reduced  to  its  equal,  ^  ?    Explain  by 
diagram. 


COMMON  FRACTIONS  41 

Changing  the  forms  of  fractions  without  chang- 
ing their  value  is  called  reduction  of  fractions. 


PRINCIPLE  TO  BE  REMEMBERED 

Dividing  both  the  numerator  and  the  denomi- 
nator of  a  fraction  by  the  same  number  does  not 
change  the  value  of  the  fraction.  This  process 
reduces  the  fraction  to  lower  terms. 


Reduction  of  Fractions  to  Lower  Terms 
56.   Reduce  to  lower  terms  : 


1. 


6 
9* 

Process         Explanation.  —  Cancel  from  the  nu- 
merator and  the  denominator  the  common 


2 
9     3 


factor  3.  This  leaves  the  factor  2  in  the 
numerator  and  3  in  the  denominator. 
The  fraction  is  thus  reduced  to  lower 
terms. 

«4  'a3  4.4  r2  fi2 

2.     3  3.     3-5  4.      g  5.    ^  6.     3-2 

7.    3^  8.     3^  9.     If  10.     I  11.     f 

12.     I  13.     I  14.     ^  15.     3-^2  16.     i\ 

Written  Exercise 

57.  1.  Reduce  to  lowest  terms.  Cancel  from  the 
numerator  and  the  denominator  all  the  common 
factors. 

10      10      10.      10.     _8_   '   12.      14 
18      12      16      20      16      16      16 

_8_      14      16.      18.      20  1_2.      12. 

12      32      42      42      32      22      18 

14      2  0      2  2      2  6.      2.8      2  5      4  2 
28      48"      88      39      56      3"0      5F 


42  INTERMEDIATE  BOOK 

2.    Cancel  from  the  numerator  and  the  denomi- 
nator all  the  common  factors. 

25 


¥ 

n 

a 

H 

¥ 

u 

n 

M 

u- 

M 

A  fraction  is  in  its  lowest  terms  when  the  numer- 
ator and  the  denominator  do  not  contain  a  common 
factor. 

Reduction  of  Improper  Fractions 

58.  1.  How  many  bushels  in  ^-  bu.  ?  How 
many  whole  bushels  ?     What  fraction  is  left  over  ? 


i/bu.  =2| 

bu.= 

=  2i  bu. 

In  the  same  manner  reduce 

2.   ^  in. 

3.  y-yd. 

4. 

1  lb. 

5. 

ttbu. 

6.   f  da. 

7.    Vtir. 

8. 

Vib. 

9. 

11  T. 

10.   I^mi. 

11.   ffyr. 

12. 

ffmo. 

13. 

-V-  bbl. 

14.    ^wk. 

15.    y-  sec. 

16. 

¥ 

17. 

U 

18.   ft 

19.    M 

20. 

fi 

21. 

ih 

To  what  whole  number  and  what  fraction  is  each 
equivalent  ? 

Oral  Problems 

59.   1.    John  has  21  dimes  in  the  bank.     How 
many  dollars  h'as  he  ? 

2.    In  a  bin  there  are  9   pk.  of  wheat.     How 
many  bushels  are  there  in  the  bin  ? 


COMMON  FRACTIONS  43 

3.  A  board  is  38  in.  long.  What  is  its  length  in 
feet  ? 

4.  A  roll  of  paper  is  43  ft.  long.  How  many 
yards  long  is  it  ? 

5.  How  many  strips  of  cloth,  each  10  in.  wide, 
may  be  cut  from  a  piece  of  cloth  36  in.  wide  ? 

6.  A  straight  section  of  road  is  4  rd.  wide  and 
100  rd.  long.  How  many  square  rods  in  the  sec- 
tion ? 

7.  A  roll  of  paper  is  f  of  a  yard  wide.  How 
many  feet  wide  is  it  ? 

8.  A  roll  of  paper  is  27  in.  wide.  How  many 
strips  each  8  ft.  long  must  be  taken  from  the  roll 
in  order  to  paper  a  wall  16  ft.  long  and  8  ft.  high  ? 

To  Reduce  a  Fraction  to  a  Mixed  Number 
60.   Reduce  to  a  mixed  number : 

1       121 

■^-     13  • 

Process  Explanation.  —  In  one  unit  there 

^Y3  ^1"^  if-     1^1  the  fraction  ^^  there  are 

13)121  as  many  units  as  13  is  contained  in 

117  121'  c»r  9  and  4  remainder.     The  re- 

J  mainder  is  written  as  a  fraction  ^. 

o       385  o496  ^578  k       T  5. 

6       8_9J_  7       901  «       8_91  q       1050 

**•       2  5  ^-2  6  ^-2  7  ^-6  7 

in      -67  5  tt837  i«       912  no       64  7 


44  INTERMEDIATE  BOOK 

To  Reduce  Whole  Numbers  to  Improper  Fractions 

Oral  Exercise 

61.  1.    How  many  halves  in  1  unit  ? 

2.  How  many  halves  in  2  units  ? 

3.  How  many  halves  in  5  units  ? 

4.  How  many  thirds  in  1  unit  ? 

5.  How  many  thirds  in  2  units  ? 

6.  How  many  thirds  in  4  units  ? 

7.  How  many  fourths  in  one  ? 

8.  How  many  fourths  in  two  ? 

9.  How  many  fourths  in  five  ? 

10.    Tell  how  to  reduce  a  whole  number  to  a 
fraction  having  a  given  denominator. 

Written  Exercise 

62.  Reduce : 

1.  16  to  halves. 

Jp  ID /-v  i^  ■p*  a  c 

-t  _2.  Explanation.  —  In  one  unit  there 

1A      2      are  two  halves.     In  16  units  there  are 
lb  =  lb  X  2     ^g  ^^        2  halves,  or  32  halves,  or  ^^. 

—  32  '  2 

""    2 

2.  24  to  halves.  3.  25  to  halves. 
4.  27  to  halves.  5.  29  to  halves. 
6.  36  to  halves.  7.  39  to  thirds. 
8.  38  to  thirds.  9.  45  to  thirds. 

10.    47  to  thirds.  ii.    49  to  thirds. 


COMMON  FRACTIONS  45 

12.  56  to  fourths.  13.  57  to  fourths. 

14.  58  to  fourths.  15.  59  to  fourths. 

16.  64  to  fourths.  17.  75  to  eighths. 

18.  87  to  tenths.  19.  99  to  twelfths. 

20.  117  to  elevenths.  21.  100  to  tenths. 

Oral  Problems 

63.  1.    How  many   quarters  will   a   person   re- 
ceive in  change  for  a  $  2.00  bill  ? 

2.  How  many  dimes  will  be  received  in  change 
for  a  $5.00  bill? 

3.  How  many  eighths  of  an  inch  are  there  in 
12  in.? 

4.  How  many  sixteenths  of  a  pound  are  there  in 
2  lb.? 

5.  How  many  eighths  of  a  gallon  are  there  in 
2  gal.  ? 

To  Reduce  a  Mixed  Nximber  to  an  Improper  Fraction 
Oral  Exercise 

64.  1.    How  many  halves  in  one  ?     In  1|  ? 

2.  How  many  thirds  in  one  ?     In  2f  ? 

3.  How  many  fourths  in  one  ?     In  3|-  ? 

4.  How  many  fifths  in  one  ?     In  2|  ? 

5.  How  many  eighths  in  one  ?     In  4|-  ? 


46 


INTERMEDIATE  BOOK 


Written  Exercise 
65.   Reduce  to  an  improper  fraction : 
1.   4f. 

Explanation.  —  The  denomi- 
nator of  the  fraction  in  the  mixed 
number   4|   is   5.      Reduce   4   to 
fifths.     Add  the  fraction  f .     The 
^^  ~  "5"  "^  5^  ~  "5~  mixed  number  4|^  =  -2^. 


Process 
43  =  4  +  3 
4  =  4xf  =  -2g^ 


6. 


10. 


14.     101 


3.  21 

7.  6f 

11.  101 

15.  20^ 


H 


8.     7| 

12.   30| 


5    41 

9.     8i- 


13. 


60| 


16.     4O3-V  17.     73-% 


Written  Exercise 
66.   Change  to  improper  fractions  : 
1.    " " 

6. 

11.  Change  to  sixths  :  25,  63,  75,  76J^. 

12.  Change  to  eighths :  14,  24,  48,  321 


151 

2.  120f 

3.  107f 

4.  631 

5.  131 

89A 

7.  601 

8.  63f 

9.  125f 

10.  75,^ 

To  Reduce  a  Fraction  to  Higher  Terms 

Oral  Exercise 

67.   1.    Examine  the  drawing  of 
the  square. 

2.  Show  by  diagram  that  J  =  f . 

3.  Make    a   diagram    to    show 

fVij,fi_3.    1—4     1__5_ 
tuctu  2"~6'    2~"8'  2~'10* 


COMMON  FRACTIONS  47 

4.  To  change  |  to  sixths,  make  the  denominator 
of  the  new  fraction  6.  To  make  the  denominator 
of  the  fraction  6,  multiply  both  terms  of  ^  by  3. 
Thus:  ix|=f. 

5.  By  what  number  must  both  terms  of  ^  be 
multiplied  to  change  the  fraction  to  eighths  ? 
Ix?^  ? 

2  X  ?     8* 

Oral  Exercise 
68.    Give  the  answers  : 
1. 

3. 
5. 
7. 
9. 


13. 


2   4   6   8-10 

2. 

1  __  ?  _  ?  _  ?  _  ? 
3   6    9   12   IS" 

2  _  ?  _  ?  _  ?  _  ? 

3  6    9   12   IS 

4. 

19       9        9        9 

4   8   12   16-20 

3  _?_?_?_  ? 
4-8-T6-T2-24 

6. 

2  _?_?_?_  ? 
5  -10-15  -20-2^ 

3  _?_?_?_  ? 
5-10-  20-12-15 

8. 

4        9         9          V         9 

5"— to  —  2^— 3^— IT 

6-12-24-18-30 

10. 

5  _?_?_?_  ? 

6  —  12  —  24  —  18  —  3T5" 

■^   ?        ?        V        ? 

8   16  ~  32   24  —  40 

12. 

3  _?_?_?_  ? 
8  —  16  —  32  —40"- 24 

5  _?_?_?_  ? 
8  — 24  "32  — 40  — 16 

14. 

7  _?_?_?_  ? 

8  —40  —  24— T6"—  32 

Written  Exercise 
69.   Change  to  the  required  denomination : 
1.   ^,  |-,  I,  1,  2  to  sixths. 

2-  h  h  h  h  h  ^  to  twelfths. 

3-  i  h  h  h  h  1  to  twelfths. 
*•    h  h  h  h  h  4  to  eighths. 

s-    h  A»  h  h  f  to  twenty-fourths. 


48  INTERMEDIATE  BOOK 

Fractions  having  the  same  denominator  are 
called  similar  fractions. 

In  order  to  compare  the  vahies  of  fractions,  to 
add  or  to  subtract  fractions,  we  must  first  reduce 
the  fractions  to  similar  fractions. 

To  Reduce  a  Fraction  to  Higher  Terms 

Oral  Exercise 

70.   1.    Change  f  to  eighths. 

Explanation.  —  To     change 
Process  fourths   to  eighths,  make  the  de- 

3      3x2      6      nominator  of  the  new  fraction  8. 
4.  ~  4  y  9  ~  ft      ^^  make  the  denominator  8,  mul- 
tiply   both    terms    of  the   fraction 
by  2. 

2.  Change  2J  to  tenths. 

Process  Explanation.  —  Reduce  the 

o^  _  ]i  mixed  number   to  an  improper 

11  '  11x2     22    ^^^^^^^"- 

—  = =  —         To   change  fifths   to   tenths, 

O         O  X  Z        lU     njake   the   denominator  of   the 
new  fraction  ten.      Then  mul- 
tiply both  terms  by  the  factor  that  will  give  the  re- 
quired denominator. 


AN   IMPORTANT   PRINCIPLE   IN   FRACTIONS 

Multiplying  both  terms  of  a  fraction  by  the 
same  number  does  not  change  the  value  of  the 
fraction. 


COMMON  FRACTIONS.  49 


Written  Exercise 

71. 

Reduce : 

1. 

1 

1 

1 

li 

2| 

2. 

i 

1 
4 

i 

H 

2i 

3. 

\ 

i 

f 

1 

4| 

4. 

\ 

i 

2 
5 

f 

f 

5. 

1* 

3i 

If 

3f 

5^ 

6. 

\ 

i 

1 

1 

4 

1 

7. 

4i 

121 

5f 

16i 

10| 

8. 

i 

i 

i 

* 

A 

9. 
10. 

tV 

lOf 

4i 

3| 
1^ 

lA 

A 

11. 

A 

7 
10 

A 

A 

i& 

12. 

i 

i 

1 

J 

i 

13. 

#0 

2lr 

A 

A 

A 

14. 

4 
25 

7 
23" 

M 

*§ 

H 

to  sixths, 
to  eighths, 
to  twelfths, 
to  tenths, 
to  tenths, 
to  sixteenths, 
to  sixteenths, 
to  twentieths, 
to  twentieths, 
to  hundredths, 
to  hundredths, 
to  hundredths; 
to  hundredths, 
to  hundredths. 


Least  Common  Denominator 

72.  Heretofore  easy  fractions  were  considered, 
the  least  common  denominator  of  which  could  be 
told  at  sight. 

Now  we  proceed  to  explain  the  process  of  dis- 
covering the  least  common  denominator  when  it 
cannot  be  readily  recognized  at  sight. 

1.  Find  the  least  common  denominator  (Led.) 
of  A   5   _i_ 

^-^  4'   8?  12- 


60  INTERMEDIATE  BOOK 

Find  the  prime  factors  of  each  denominator. 

Thus:  ^^2-2 

8=2-2-2 
12  =  2-2       .3 


The  Led.  must  contain  the  prime  factor  2  three 
times,  or  it  would  not  be  exactly  divisible  by  8. 

The  1.  c.  d.  must  contain  the  factor  3  once,  or 
it  would  not  be  exactly  divisible  by  12. 

Hence  the  1.  c.  d.  is  2  x  2  x  2  x  3  =  24. 

Factor  each  denominator  and  take  each  prime 
factor  the  greatest  number  of  times  it  occurs  in 
any  denominator. 

2.  Find  the  1.  c.  d.,  if  the  given  denominators 
are  4,  6,  16. 


We  have : 


4=2.2 
6  =  2 
16=2.22. 2 


The  1.  c.  d.  must  contain  the  factor  2  four  times. 
The  Led.  must  contain  the  factor  3  once. 
Hence  the  1.  c.  d.  is  2  x  2  x  2  x  2  x  3  =  48. 

3.    If   the  denominators   are  4,  9,  12,  find  the 
Led.  ^^2-2 

9  =  3.3 

12  =  2. 2. 3 
Hence  the  1.  c.  d.  =  2  x  2  x  3  x  3  =  36 


COMMON  FRACTIONS  61 

Written  Exercise 

73.  Find  the  1.  c.  d.  of  the  following  denomina- 
tors : 

4.    2,  6,  36.  5.   3,  4,  16,  20. 

6.  9,  24,  36.  7.  10,  20,  25. 

8.  15,  8,  30.  9.  20,  15,  30. 

10.  7,  49,  6.  11.  8,  6,  9,  36. 

12.  12,  16,  36.  13.  16,  18,  12. 

Written  Exercise 

74.  Find  the  common  denominator  : 

l23.5  o       S      i      1  o311 

^'     3?    5'    8  ^'     4'    Ef    6  ^'     5"?    2?   "8" 

15.1  553.      5.  fi732 


^'     4?    9?    3  ^'     8'    4?    6  ^'     8^    3jJ?    ^S" 

7_5_AJL  q357  q54 

'•     12>    6?    8  **•     TO'    6'    2"0'  ^-     2T'    Tj 

10  -^        3   _27._      n   _5     25      80 
•^"-  10?  100?  10  0  0      "•  1F05  IFOO^?  10000 


Oral  Exercise 
75.   1.    What  are  similar  fractions  ? 

2.  Change  ^  and  J  to  fractions  having  a  common 
denominator. 

3.  Change  ^,  J,  and  ^  to  fractions  having  a  com- 
mon denominator. 

4.  Change  ^  and  ^  to  fractions  having  a  common 
denominator. 

5.  Change  ^,  J,  and  ^  to  fractions  having  a  com- 
mon denominator. 


52  INTERMEDIATE  BOOK 

6.  Change  ^,  f ,  and  |-  to  fractions  having  a  com- 
mon denominator. 

7.  Change  ^,  f ,  and  f  to  fractions  having  a  com- 
mon denominator. 

8.  Tell   how   to  change    fractions  to   fractions 
having  a  common  denominator. 

Study  Exercise 

76.   1.    Reduce  ^,  f,  and  f  to  similar  fractions; 
that  is,  to  fractions  having  the  same  denominator. 

Explanation. — By  inspection  we  find 
Process     ^j^^t  these  fractions  may  all  be  reduced  to 
1  =  ^       twelfths. 

t=A  fit 

2.    Reduce  to  similar  fractions :  ^,  f,  -f^^  A 

Process 
Find  the  least  common  denominator 

3  =  3 

4  =  2x2 

12  =  2x2x3 

16=2x2x2x2 
1.  c.  d.  =  2  X  2  X  2  X  2  X  3 
The  least  common  denominator  is  48 
Then48H-3=16       1x16^16 
3x16     48 


3x12 

36 

4x12 

48 

5  x4 

20 

12x4 

48 

9  x3_ 

27 

16x3 

48 

COMMON  FRACTIONS  53 

48^4  =  12 

48-^12  =  4 

48^16  =  3 

Explanation.  —  48  is  the  1.  c.  d.  Change  the  de- 
nominator of  the  fraction  to  48.  Multiply  both  terms 
of  the  fraction  ^  by  16.  Multiplying  both  terms  of  the 
fraction  by  16  does  not  change  the  value  of  the  fraction. 

Proceed  in  like  manner  with  the  fractions  f ,  ^^,  and  ^. 

3.   Reduce  If,  ^q,  f  to  similar  fractions. 

Explanation. — Reduce  the  mixed 

number,  1|,  to  the  improper  fraction. 

Process        4*     ^'^^^  ^^  inspection  or  by  factoring 

the  least  common  denominator  (1.  c.  d.). 

The  1.  c.  d.  =  30. 


12.^  5.^50 
■*-o         o  —  Q  n 


7  7  2  1 

iT  ~  To  ~  3^7       The   fractions  must  be  reduced  to 
1  =  1  =  11       thirtieths. 

1^  =  1* 

4_24 
5~30 

These  fractions  have  a  common  denominator; 
hence,  they  are  similar  fractions. 
Tell   how  to  add  similar  fractions. 

Written  Exercise 
77.   Reduce  to  similar  fractions  : 
1.  h  h  I-  ^-  h  h^ 


64  INTERMEDIATE  BOOK 

5. 

7. 

9. 
11. 
13. 
15. 

Oral  Exercise 
78.   Reduce   to   similar   fractions  and  compare. 


h  h  3 

6. 

A?    8'    T^ 

hhi 

8. 

15'    12'   TTT'   ¥ 

7       4        8 

9'  s^  rg" 

10. 

TO'    30"'    T^'    2^0" 

Toy    25'    5" 

12. 

T'   A'   1'   1 

h  h  h  1 

14. 

1^6'    4'    8'    A 

2        7        5        9 
5?    10'    6'    20 

16. 

2^0'    sV'    T5-'    12 

Which  is  the  larger  ? 

1.   1  and  ^           2. 

A  and  1 

3. 

i  and  1- 

4.    f  andf           5. 

T2  and  3-6^ 

6. 

|and| 

7.   f  and  1           8. 

landf 

9. 

fandf 

Addition  of  Fractions 
79.   1.    Add  I  and  |,  J  and  J,  ^  and  1 

2.  What  is  the  common  denominator  of  ^  and 
J?landl?iandi? 

3.  Change  J  and  ^  to  similar  fractions. 

4.  Change  J  and  ^  to  similar  fractions. 

5.  Change  ^  and  ^  to  similar  fractions. 

6.  Change  ^  and  ^  to  similar  fractions. 

7.  Tell  how  to  add  J  and  ^,  ^  and  J,  ^  and  J. 

8.  What  is  the  sum  of  ^  and  ^  ?     f  and  f  ? 

9.  Name  four  common  denominators  of  ^  and  f . 
10.    What  is  the  least  common  denominator  of  ^ 

andf? 


COMMON  FRACTIONS 


55 


Written  Exercise 
80.   1.    Show  by  the  dia- 
gram that  I  +  ^  =  f . 

o        1  _    ?    .     " 


Wa 


m 


6  ' 


2^3  —  6- 


3.  Can  you  show  by  a 
diagram  that  i^  +  i^  =  f  ? 

4.  Can  you  show  by  dia- 
gram that  i+i+^=l? 

5.  Can  you  show  by  diagram  that  ^  +  -3  =  1^? 


Hl= 

=  A? 

Written  Exercise 

81. 

Add: 

1. 

1  and  I. 

Pkooess 

(1) 

The  common  denominator  is 

24. 

(2) 

5  5x4 

6  6x4 

20 
24 

7_7x3 
8     8x3' 

21 
24 

(3) 

24)41 

11^  Ans. 

Explanation.  —  (1)  Find  the  common  denominator 
by  inspection  or  by  factoring. 
(2)  Reduce  the  fractions. 


56  INTERMEDIATE  BOOK 

(3)  Add  the  numerators  of  the  similar  fractions. 
Place  the  sum  over  the  common  denominator. 

(4)  Reduce  this  fraction  to  a  whole  or  a  mixed 
number. 

What  other  common  denominator  might  have 
been  used?  Why  is  the  least  common  denomi- 
nator the  best  denominator  to  use?  Why  is  it 
called  the  least  common  denominator  ? 

Written  Exercise 
82.    Add,  using  pencil  only  v^hen  necessary  : 
1. 

5. 


13. 


83.    Add: 
1. 

4. 


10. 


Written  Problems 

84.  1.  A  boy  earned  $  f  one  day,  $  f  another 
day,  and  $-|  the  third  day.  How  much  did  he 
earn  in  the  three  days  ? 


i+^- 

2. 

l+i 

3. 

i+i 

4. 

i+i 

1+4 

6. 

f+f 

7. 

4+i 

8. 

4  +  T^ 

f+A 

10. 

l+f 

11. 

i+l 

12. 

i+* 

f+f 

14. 

i+l 

15. 

i+A 

16. 

i+l 

Written  Exercise 


i+l 

2. 

*+l 

3.    l+j^ 

t  +  ^'tr  +  i 

5. 

f+A+i 

6-    l  +  A  +  l 

M+i4+A 

8. 

Hf  +  f 

9-    f+l  +  xV 

H+tt+A+ 

9 
10 

11. 

1^  +  l  +  tt  +  f 

COMMON  FRACTIONS  57 

2.  During  the  forenoon  four  observations  of  the 
thermometer  were  made.  At  the  first  reading  the 
temperature  was  50°;  twenty  minutes  later  it 
showed  an  increase  of  1°;  twenty  minutes  later  it 
had  increased  |^°  more;  and  at  the  last  reading 
it  had  raised  |-°  more.  What  was  the  temperature 
at  the  last  reading  ? 

3.  If  the  length  of  a  book  is  ^  ft.  and  the  width 
^  ft.,  what  is  the  length  of  both  sides  and  both 
ends  of  the  book  ? 

4.  A  farmer  gathers  J  doz.  eggs  the  first  day, 
f  doz.  on  the  second  day,  and  ^  doz.  on  the  third 
day.  How  many  eggs  did  he  gather  in  the  three 
days? 

5.  A  clerk  cut  3  pieces  from  a  roll  of  ribbon. 
The  first  piece  was  ^  yd.,  the  second  ^  yd.,  and 
the  third  f  yd.  What  was  the  total  length  cut 
from  the  roll  ? 

Addition  of  Mixed  Numbers 


s. 

Add  at 

sight : 

1. 

10| 

2.  301 

3.  50f 

4. 

70f 

6* 

15| 

25i 

lOf 

5. 

901 

6.  201 

7.  301 

8. 

40*. 

10i_ 

lOi 

101 

l4 

9. 

80| 

10.  67f 

11.  591 

12. 

361 

lOi 

15^ 

111 

14* 

58  INTERMEDIATE  BOOK 

13.  46|    14.  831    15.  144|   16.  760| 
5*       81       671      1871 


17.  2651   18.  4721   19.  34f   20.  144f 
3211       691      768       793 
871      9671      251      471 


Written  Exercise 


86.   Add: 


1.    43fandl9|. 

Explanation.  —  Add   the   frac- 
Process         tions.     The    least   common   denomi- 
nator is  15. 


43 1=   43^^ 
791=    79+f 

Add  integers 

l^V     Write 

3. 

-^■ 

123A 

Find  the  sum  of  the 

integers  and 

the  fractions. 

2.     14|             3. 

113f 

4. 

761 

5. 

123| 

5f 

19f 

47i 

Hi 

6.     3O1V          '• 

706| 

8. 

lOOf 

9. 

i^m 

241 

69i 

79f 

94| 

10.   43if      11. 

lllH 

12. 

87511 

13. 

405^ 

SVcr 

22| 

691 

131 

14.    763|      15. 

108| 

16. 

95tV 

17. 

78| 

45* 

45i 

36 

97f 

COMMON  FRACTIONS  59 

Written  Exercise 
87.    Add: 

1.  75|  2.  79f  3.  761    4.  701|  5.  lOlJ 
461    63|    401       671     67f 


6. 


11. 


46f 

7. 

79| 

8. 

101^   9.  780|  10.  167i 

231 

631 

67J^     63f     98 

291 

12. 

65| 

13. 

49|   14.  987|  15.  787| 

381 

79f 

58|     769|    868| 

47f 

87f 

67tV     898|    979| 

56| 

98i 

86|      654|    6973-'5 

Written  Problems 

88.  1.  Mr.  Edwards  sold  IQl  bii.  of  wheat  to 
one  man  and  4f  bu.  to  another.  How  many 
bushels  did  he  sell  to  both? 

2.  An  agent's  expenses  were  $  4|  the  first  day, 
$  3^  the  second  day,  and  $  3f  the  third  day.  What 
is  the  total  amount  of  his  expenses  for  the  three 
days? 

3.  Robert  worked  f  of  the  day  Monday,  ^  of 
the  day  Tuesday,  1  of  the  day  Wednesday,  and  |  of 
the  day  Thursday.     How  many  days  did  he  work  ? 

4.  A  girl  studied  21  hours  Monday,  IJ  hours 
Tuesday,  31  hours  Wednesday,  2|  hours  Thursday, 
and  ^  hour  Friday.  How  many  hours  did  she 
study  in  all  ? 


60  INTERMEDIATE  BOOK 

5.  A  jointed  fishing  pole  has  3  sections.  The 
first  section  is  2^  ft.  long,  the  second  is  2|-  ft.,  and 
the  third  is  3  ft.     How  long  is  the  pole  ? 

6.  A  field  is  80f  rd.  long  and  40|-  rd.  wide. 
How  many  rods  of  fence  are  required  to  inclose  the 
field? 

7.  The  ice  for  a  family  weighs  20^^  lb.,  22|  lb., 
18i  lb.,  25f  lb.  Find  the  total  weight  of  ice  used 
in  four  days. 

8.  A  painter,  working  by  the  hour,  works 
6|-  hr.  the  first  day,  S^  hr.  the  second  day,  8^  hr. 
the  third,  7f  hr.  the  fourth,  and  4  hr.  the  fifth 
day.  How  many  hours  did  he  work  in  the  five 
days  ? 

Subtraction  of  Fractions 

89.  1.    What  is  the   difference  between   |  and 
1?   I  audi?   fandi?   f  andl? 

2.  Change  ^  and  J  to  similar  fractions. 

3.  Change  f  and  ^  to  similar  fractions. 

4.  Change  |  and  ^  to  similar  fractions. 

5.  Tell  how  to  subtract  J  from  f . 

6.  Tell  how  to  subtract  ^  from  f. 

7.  Tell  how  to  subtract  ^  from  f. 

8.  Tell  how  to  subtract  f  from  f. 

9.  Explain  how  to  subtract  similar  fractions. 
10.  Make  a  rule  for  subtracting  fractions  that 

are  not  similar. 


COMMON  FRACTIONS 


61 


Written  Exercise 
90.    1.    Show  by  the  diagram  that  |  — 1-  =  ^-. 


2. 


2.__L  .     1  — X  . 
3  ~  6  '    2  "~  6  ' 

2._i_  J. 

3         2  ~  6* 


3.  Can  you  show  by  dia- 
gram that  |-i  =  J? 

4.  Can  you  show  by  diagram  that  1  —  i^  —  i  =  i? 

5.  Can  you  show  by  diagram  that  f  —  i  =  ^2  ^ 


Oral  Exercise 

91.   Subtract: 

1.    1-i 

2.     1-1 

3.     1-i 

4.     1-1 

5.    1-J 

6.     1-1 

7.     1-t 

8.     1-^ 

9-   i-i 

10.     f-J 

11.     f-i 

12.     i-i 

Oral  Problems 

92.  1.  What  is  the  difference  between  J  of  an 
apple  and  ^  of  an  apple  ? 

2.  What  is  the  difference  between  ^  lb.  and 
ilb.? 

3.  In  a  bin  there  are  If  bu.  of  potatoes.  If 
J  bu.  is  taken  from  the  bin,  how  many  bushels 
remain  ? 

4.    From  a  roll  of  cloth  12^  yd.  long  a  salesman 
cut  41  yd.     How  many  yards  remained  in  the  roll? 


62  INTERMEDIATE  BOOK 

5.  The  distance  between  two  villages  is  4  mi. 
If  a  house  is  1|  mi.  from  one  village,  how  far  is 
it  from  the  other  ? 

6.  From  a  piece  of  cheese  containing  3f  lb.  a 
grocer  sold  2^  lb.     How  many  pounds  remained  ? 

7.  A  farmer  has  two  fields.  One  field  contains 
20 J  A.  The  other  field  contains  4^  A.  less.  How 
many  acres  in  the  smaller  field  ? 

8.  From  a  piece  of  steak  weighing  4^  lb.  a 
butcher  cut  |  lb.,  J  lb.,  and  ^  lb.  How  many 
pounds  of  steak  has  he  left  ? 

9.  From  a  gasoline  tank  containing  20  gal., 
41  gal.,  2^  gal.,  and  3  gal.  were  drawn.  How 
many  gallons  were  left  in  the  tank  ? 

10.  A  carpenter  had  a  piece  of  molding  4^  ft. 
long,  from  which  he  cut  two  pieces,  one  2J  ft.  and 
the  other  1|  ft.  long.  How  long  is  the  piece  that 
is  left? 


1      i  — 4  2 

R  1   _    2  R 


1-1 
3        6 

1  _  1 


10. 


13.     i_x  14. 

17.     liV-l        18. 


Oral  Exercise 

imilar  i 

fractions 

and  subtract : 

i-i 

3-     i- 

■i 

4. 

2        12 

i-i 

'•    i- 

i. 

8. 

i-i 

i-iV 

11-     i- 

1 

5 

12. 

i-i 

i-i 

15.     1- 

.  _7_ 
12 

16. 

li-8^ 

H-i 

19.     If 

-t 

20. 

li-l 

COMMON  FRACTIONS  63 


Written  Exercise 

94. 

Subtract : 

1. 

271 
121 

Process 

Arrange  the  work  as 
follows : 

27i=27f 
121  =  121 

Explanation.  - 
271  =  27| 
27f  - 12^  = 

16i 

2. 

1051 

3. 

63^ 

4. 

57f 

5. 

67| 

40 

15-1 

191 

23f 

6. 

251 

7. 

751 

8. 

48f 

9. 

5^ 

131 

691 

231 

24f 

10. 

105t 

11. 

302f 

12. 

5141 

13. 

524| 

971 

67| 

86f 

^^ 

14. 

574| 

15. 

7331 

16. 

lOOX 

17. 

1000^ 

1251 

m 

601 

9011 

18. 

700-1 
5491 

19. 

487-1 

looj 

20. 

5271' 
2001 

21. 

800/^ 
4001 

22. 

501f 

23. 

lOlOf 

24. 

16261 

25. 

2000J 

109| 

700| 

448| 

llllf 

64 


INTERMEDIATE  BOOK 


Study  Exercise 
95.   Reduce  to  similar  fractions  and  subtract : 


1  from  |. 


Process 
(1)  1.  c.  d.  is  6 
/ox  2     2x2_ 
^^^  3"3x2" 

/ox  l_lx3_ 
^"^^  2"2x3" 
4_3^ 
6     6 

2.   I"  from  f . 

Process 
3^3x3^^ 
4     4x3     12 

?  =  ?x-  =  A 
3     3     4     12 

12     12     12 


Explanation.  —  To  reduce 
to  similar  fractions  multiply 
both  terms  of  the  fraction  J  by 
3  and  both  terms  of  the  fraction 
I  by  2.     Then  subtract. 

Multiplying  both  terms  of  a 
fraction  by  the  same  number 
does  not  change  the  value  of 
the  fraction.  The  difference 
between     4    and    #    is    4,    the 


answer. 


Explanation. — The  Led.  is  12. 
Multiplying  both 
terms  of  the  fraction 
by  the  same  number 
does  not  change  the 
value  of  the  fraction. 


1  ~  12 


3.    15|  from  26 1. 


Process 
26|  =26^^  =  25^1 


15# 


15^ 


T2 


loii 


Explanation.  —  Reduce  § 
and  I  to  similar  fractions. 
We  obtain  -^  and  ^.  We 
cannot  subtract  -^^  from  ■^^' 
Take   1  from   26,  and  add  it 


tOtV;  !%  +  {! 


10 
]2- 


25f| 


15-^^-  —  lO^J,  the  answer. 


COMMON  FRACTIONS  65 

Written  Exercise 

96.  Subtract: 

1.  51    2.  61    3.  81    4.  lOf   5.  7i 

03         Ql         A2  Q4        4.3. 

6.  81    7.  31    8.  12^    9.  101   10.  191 

5J     If      _34     _6i     12| 

11.  231  12.  181  13.  141  14.  151  15.  27f 
13|     9|     lOj     10|     nil 

Written  Problems 

97.  1.  A  farmer  had  30^  bu.  of  apples.  He 
sold  17f  bu.     How  many  bushels  has  he  left? 

2.  If  I  have  $  79 J  and  spend  $  51f ,  how  many- 
dollars  have  I  left  ? 

3.  A  table  is  3^  ft.  long  and  2^  ft.  wide. 
How  much  greater  is  the  length  than  the  width  ? 
Find  the  perimeter. 

4.  A  farmer  sold  105f  bu.  of  his  potato  crop, 
kept  91  bu.  for  planting,  and  used  55J  bu.  for  cook- 
ing.    How  many  bushels  in  the  crop  ? 

5.  A  4|-in.  spike  is  driven  through  a  2l-in.  board 
into  a  post.     How  far  is  it  driven  into  the  post  ? 

6.  The  time  required  to  travel  from  A  to  C  is 
28f  hr.  The  time  required  to  travel  from  A  to  B 
is  lOf  hr.  How  much  longer  does  it  require  to 
travel  from  A  to  C  than  from  A  to  B  ? 


66  INTERMEDIATE  BOOK 

7.  Along  one  side  of  a  field  80  rd.  long,  there 
is,  for  a  distance  of  37f  rd.,  a  stone  fence.  The 
remaining  distance  is  fenced  with  wire.  How 
long  is  the  wire  fence  ? 

8.  A  loaded  truck  weighs  2^  T.  The  load  con- 
sists of  two  parts.  The  first  part  weighs  IJ  T. 
the  second  |  T.     Find  the  weight  of  the  truck. 

Multiplication  of  Fractions 

98.  Give  answers  rapidly  : 

1.  How  many  fourths  are  5  times  J  ? 

2.  7  times  |  are  how  many  fifths  ? 

3.  6xf=?  4.    10x|  =  -230  =  6| 

5.    6x|  =  ?  6.    10xf  =  ?         7.  Jx6  =  ? 

8.   ix7=?  9.   1x2  =  ?        10.  ix3  =  ? 

11.    -|xi=?  12.     11x4  =  ?         13.    8xl|=? 

14.     12x11  =  ?      15.     10x1-1  =  ?      16.    12x11  =  ? 

Oral  Problems 

99.  1.    William   earns   $f   daily,    or   $ in 

6  days. 

2.  John's  step  is  ^  of  a  yard.  How  far  does  he 
go  in  6  steps  ? 

3.  George  paces  the  width  of  his  tennis  court, 
taking  10  steps.  How  wide  is  the  court,  if  his 
step  is  |-  of  a  yard  long  ? 


COMMON  FRACTIONS  67 

4.  A  father  gives  $  f  to  each  of  his  5  children. 
How  much  does  he  give  them  all  together  ? 

5.  A  man  takes  a  run  of  f  of  a  mile  every  day. 
How  many  miles  does  he  run  in  6  days  ? 

To  Multiply  a  Fraction  by  a  Whole  Niunber 
100.   1.    Multiply  I  by  64. 

Process  ^^  oa   j.-         n 

r.  Explanation.  —  64  times  | 

7      f^/<_  7x^^     may  be  written  — - — .     Cancel 

-  X  04—        -  8 

^  the  common  factor.     Why? 

=  56 

2.    Multiply  3-^2  by  64. 
Process 

16 

— -  X  64  =     ^  ^^  Explanation.  —  64  times  -^^ 

12  12  64  X  7 

\r         may  be  written  — — — .     Cancel 

7  X  16      the  common  factor  and   reduce 
""3  to  a  mixed  number. 

—  112 


=371 


To  Multiply  a  Fraction  by  a  Whole  Number 
Multiply  the  numerator  of  the  fraction  by  the 
whole  number  and  divide  the  product  by  the  de- 
nominator of  the  fraction.    Cancel  when  possible. 


68  INTERMEDIATE  BOOK 


Written  Exercise 

101. 

Solve,  using  pencil  only  when 

necessary : 

1. 

22  X 

^ 

2. 

6xf 

3. 

Txt\ 

4. 

8x 

A 

5. 

120  x  1 

6. 

360x1 

7. 

72  X 

f 

8. 

75xf 

9. 

840  xf 

10. 

960  X 

H 

11. 

42x| 

12. 

35xf 

The   sign  x  may   mean   times   or   multiply  hy. 
In  this  exercise  it  should  be  read  times. 

To  Multiply  a  Whole  Number  by  a  Fraction 
102.    Multiply  and  explain  : 


1. 

64  by  J 

2. 

96byi 

3. 

64  by  3^ 

4. 

SSby^i, 

5. 

f  times  24 

6. 

^x38 

7. 

1  times  48 

8. 

/^  times  20 

9. 

1  times  54 

10. 

1  times  42 

To  Multiply  a  Fraction  by  a  Fraction 

103.  1.  What  part  of  the  circle  is  shaded? 
Show  ^  of  the  part  that  is  shaded. 
What  part  is  this  of  the  whole 
circle  ? 

2.    Show  f  of  the  part  that  is 
shaded.     What  part  of  the  whole 
is  this?     |of  i  =  |xi  =  ? 
3.    Draw  a  circle  and  shade  ^  of  it.     Draw  lines 
from  the  center  of  the  circle  dividing  the  shaded 


COMMON  FRACTIONS  69 

part  into  4  equal  parts.     What  part  of  the  whole 
circle  is  one  of  these  parts  ?     4  of  |^  =  ? 

4.  A  boy  takes  f  of  an  apple 
and  cuts  each  quarter  into  two 
equal  parts.  What  fraction  of  the 
whole  apple  is  each  part  ? 

5.  Make  a  rule  for  the  multipli- 
cation of  a  fraction  by  a  fraction. 

ip.f3_3  iofi— 1  1  of  1  =  1 

2^  01  4-8"  4:^^2"~sr  3OJ-26 

6.  In    these   examples,   the   word   of  indicates 
multiply,     i^   of   f   means  ^  x  J,  or   f  multiplied 

The  fraction  |^  of  f  is  sometimes  called  a  com- 
pound fraction. 


Written  Exercise 

104.    1.    Find  I  of  f . 

Process 

4  ^^  F~t  ^  F         Explanation. — Write  the  frac- 
1  tions  in  the  form  for  multiplication. 

_  ^  X  5      Cancel    common    factors   from   the 
4  X  ^      numerator  and  denominator.    Write 
2     the  product  of  the  remaining  factors 
in  the  numerator  and  the  denomi- 
nator. 


1x5 

4x2 

5 

8 


Explanation.  —  Write    the    ex- 
planation. 


70  INTERMEDIATE  BOOK 

2.  Find^-Vofif. 
Process 
1       4 

3       3 

Find: 

3.  i  of  1  4.   i  of  i  5.   1  of  i 

6.     lofi  7.     loff  8.     loff 

9.     iof  I  10.    f  of  f  11.     I  of  I 

Tell  how  to  multiply  a  fraction  by  a  fraction. 
Make  a  rule  for  the  multiplication  of  a  fraction  by 
a  fraction. 


TO   MULTIPLY  A  FRACTION   BY  A  FRACTION 

Cancel  factors  common  to  the  numerators  and 
denominators  and  multiply  the  remaining  factors 
in  the  numerators  for  the  new  numerator,  and 
the  remaining  factors  in  the  denominators  to- 
gether for  the  new  denominator. 


Oral  Exercise 
105.    Solve,  using  pencil  only  when  necessary 


1-  foff 

2.    foff 

3.   fofl6 

4.    ^Xf 

5.    fxV- 

6.    ^Xf 

7.    120  x| 

8.    12x1^ 

9.     15Xj-V 

COMMON  FRACTIONS  71 

10.    63x^1^  11.    IGx^L  12.    7x48 

13.  f  Xi  14.  ^-^X^  15.  fx| 

16.  ffxf  17.  -y^-Xf  18.  3^xf 

19.  tVx^  20.  fxf  21.  2X| 

22.  2/xiJ-  23.  5xf  24.  fxf 

25.  fX-V-  26.  -V-X72  27.  |  X  3^ 

28.  V-Offf  29.  f  off!  30.  |X^ 

Explain  how  the  multiplication  of  a  whole  num- 
ber by  a  fraction  or  a  fraction  by  a  whole  number 
may  be  performed  as  if  it  were  the  multiplication 
of  a  fraction  by  a  fraction. 

Oral  Problems 

106.  1.  How  much  does  a  boy  earn  in  7  days  if 
he  makes  $  ^  in  a  day  ? 

2.  A  man  charges  $  ^  an  hour.  How  much  does 
he  earn  in  |-  of  an  hour  ? 

3.  A  boy  rides  his  bicycle  at  the  rate  of  12  mi. 
an  hour.     How  far  does  he  go  in  |-  of  an  hour  ? 

4.  Find  the  cost  of  6  chairs  at  $  If  each. 

5.  Make  a  bill  for  6  days'  wages  at  $2^  per 
day. 

6.  What  is  the  cost  of  a  piece  of  dress  goods 
containing  7  yd.  if  the  material  sells  at  $  If  per 
yard? 


72  INTERMEDIATE  BOOK 

7.  A  roll  of   wall  paper  is  f  yd.  wide.     How 
many  yards  can  be  covered  with  6  strips  ? 

8.  A  man's  expenses  were  $  4|^  per  day.     What 
were  his  expenses  for  20  da.  ? 

To   Multiply  a  Mixed   Number  by  a  Whole   Number 
or  a  Whole  Number  by  a  Mixed  Number 

107.   1.   Multiply  ^  by  8. 

Process 

8x4|=8xl^         Explanation.-— Reduce    the 
mixed  number  to  an  improper  frac- 
=  r  ^  -'-^     tion.     Proceed   as  in  multiplication 
F  of  a  fraction  by  a  whole  number. 

1 

=  38 

2.  Multiply  26  by  4|. 

Process 

42.  X  S6  =  l^  x36  Explanation.  —  Reduce     the 

^                ^19  J^ixed    number    to    an   improper 

1  i      oa  fraction.     Proceed  as  in  multipli- 

= rt"-^  cation  of   a  fraction   by  a  whole 

^  number. 

=  168 

3.  Multiply  39  by  4f . 

Process  Explanation.  —  Reduce     the 

4^  X  39  =  -2^'*  X  39  mixed    number    to    an   improper 

24  X  39  fraction.     Proceed  as  in  multipli- 

^        ^  cation  of   a   fraction  by  a  whole 

=  1871  number. 


COMMON  FRACTIONS 


73 


Written  Exercise 
108.   Multiply,  using  pencil  only  when  necessary : 


1. 

2|x4 

2. 

3|x8 

3. 

4^x5 

4. 

12xlf 

5. 

14x3f 

6. 

17x4f 

7. 

25  X  3| 

8. 

48  X  4,^ 

9. 

7fxl5 

10. 

271x20 

11. 

48f  X  40 

12. 

56fx60 

13. 

100  X  2| 

14. 

450x1 

15. 

600  x  5f 

To  Multiply  a  Mixed  Number  by  a  Fraction  or  a 
Fraction  by  a  Mixed  Number 


109.    Multiply 
1.   iby20|. 


Process 


5x201 


_^ 


31 


i  ^ 


2. 

5. 

8. 
11. 
14. 


_  31 

=  151 
2fx| 
3fxi 
4|xf 
11x101 
|x4| 


Written  Exercise 


Explanation.  —  Reduce  the 
mixed  number  to  an  improper  frac- 
tion and  multiply.  Cancel  where- 
ever  possible. 


3. 

6. 

9. 
12. 
15. 


6ix| 
2|xi 
7fxf 
fJxSf 
¥  X  T| 


4. 

3fx^ 

7. 

3fxJ 

10. 

5fx| 

13. 

i|x6i 

16. 

¥x20i 

74 


INTERMEDIATE  BOOK 


To  Multiply  a   Mixed   Number   by  a  Mixed  Number 
110.   Multiply: 
i.    9|byl5i 
Process 

13     23 


2 


—  299 

=  149i 

31x41 
7|x6t 
48fx24| 
66f  X  331 


2. 

5. 

8. 

11. 


Explanation.  —  Reduce  the 
mixed  number  to  improper  frac- 
tion and  multiply.  Cancel  where 
possible. 


3. 

6. 

9. 

12. 


51x1^ 


17fx 


11^ 
^^3 


331 X  3i^\ 
ixl6| 


4. 

7. 
10. 
13. 


21x51 

191x28^ 
161x161 
33|^  X  3y% 


Written  Problems 

111.  1.  Theodore  earns  $  4^  a  week  for  7  weeks. 
How  many  dollars  does  he  earn  ? 

2.  James  works  13  J  hr.  at  30^  an  hour.  How 
much  does  he  earn  ? 

3.  A  plumber  charges  $^  per  hour  for  his 
time.     How  much  does  he  get  for  3  hours'  work  ? 

4.  An  engineer  charged  $  b^  a  day  for  work 
that  occupied  him  13^  days.  How  much  was  his 
bill? 

5.  What  is  the  cost  of  13^  doz.  eggs  at  $;^  a 
dozen  ? 


COMMON  FRACTIONS  *  75 

6.  John  is  5^  ft.  tall.  James  is  only  ^  as  tall 
as  John.     How  tall  is  James  ? 

7.  For  9  years  a  boy  has  spent  J  of  every  year 
in  school.  How  many  years  has  he  spent  in 
school  ? 

8.  If  pepper  sells  at  15^^  a  pound,  find  the 
cost  of  1^  bags,  weighing  120  pounds  each. 

9.  A  boy  invests  $  26^  in  pigeons.  At  the  end 
of  a  year  he  gains  ^  of  his  investment.  What  is 
his  gain? 

10.  When  wheat  is  S5^^  a  bushel,  how  much 
will  205  bushels  bring  ? 

11.  Theodore's  wages  are  |  of  his  father's.  What 
does  Theodore  receive,  if  his  father  earns  $  22  a 
week  ?     If  his  father  earns  $  17|-  a  week  ? 

12.  If  a  cord  of  wood  cost  $  31,  what  will  5J 
cords  cost  ? 

13.  William  has  spent  ^  of  his  weekly  allowance. 
He  has  $  2^  left.     What  is  his  weekly  allowance? 

14.  At  5^  per  square  foot  what  is  the  cost  of 
painting  an  advertisement  upon  a  wall,  IS^  ft.  by 
5i  ft.  ? 

15.  A  grocer  having  16|-  crates  of  berries  sold 
f  of  them,  or crates. 

16.  Find  the  cost  of  125  tons  of  lignite  coal  at 
$  5|-  a  ton. 


76  INTERMEDIATE  BOOK 

Practical  Problems  —  Area 

112.  1.  How  many  square  feet  in  the  area  of  a 
rectangle  lOf  ft.  long  and  3|-  ft.  wide  ? 

Explanation. — In  finding  the 
product  of  the  base  and  the  alti- 
tude, indicate  the  operations,  and 
then  cancel  factors  common  to 
the  numerator  and  denominator. 
Not  until  after  this  is  done  should 
the  multiplications  be  performed. 
In  this  example,  the  indicated  area 

is  *-^ —  sq.  ft.     Cancel  the  fac- 

3x4 

tors  and  multiply. 
Find  the  area  of  a  rectangle  7^  ft.  long  and 

4 J  ft.    long   and   half  as  wide. 

4.  The  area  of  a  garden  is  30f  sq.  yd.  If  an 
area  f  as  large  as  the  garden  be  added  to  it,  how 
many  square  yards  larger  will  it  be  ? 

5.  A  rectangle  has  a  base  64  ft.  long  and  an 
altitude  36^  ft.     Find  its  area. 

6.  The  base  of  a  rectangle  is  f  of  a  foot,  its 
height  is  f  of  a  foot.     Find  its  area. 

7.  How  many  square  feet  are  there  in  the  sur- 
face of  a  trunk  4  feet  long,  f  of  a  foot  wide,  and 
f  of  a  foot  high  ? 


Pkocess 

8 

5 

^^ 

x;i:^_40 

1 

X  ^        1 
1 

=  40 

The  answer  is 

40  sq. 

.ft. 

2. 

Find  the  ai 

Hit. 

wide. 

3. 

A   table   is 

How  wide  is  it  ? 

COMMON  FRACTIONS  77 

8.  A  border  is  |-  of  a  yard  wide  and  4  yd.  long. 
What  is  its  area  in  square  yards  ? 

9.  A   room  is    25    ft.    long  and  17|-  ft.  wide. 
What  is  the  area  of  the  floor? 

10.  A  room  is  44  ft.  by  20 J  ft.  What  is  the 
area  of  the  floor  ? 

11.  A  room  is  8  ft.  high,  16  ft.  long,  and  12  ft. 
wide.  What  is  the  area  of  the  four  walls  ?  What 
is  the  area  of  the  floor  and  ceiling  ? 

Written  Exercise 
113.   1.    Find  the  product  of  f,  f,  and  |. 

Pjrocess  Explanation. — In  multipli- 

cation  of    fractions,   it    is   best 
merely  to  indicate  the  operations 


% 


L- c  =  _  Ans.      at    first,   then   to   cancel    equal 

^  X  p  X  y      y  factors    in    the    numerator   and 

r  denominator. 

2.    f  off  off  3.    fxfofl 

4.    f  0f|0f|  5.    ^^^i-^l 

8.    Ij0f|0ff0ff  9.     1|  of  I  Of -1/  Of  i 

10.     12x8  of  fix  ^ 

A  fraction  of  a  fraction  is  called  a  compound 
fraction,  f  of  ^  and  f  of  f  of  f  are  compound 
fractions. 


78 


INTERMEDIATE  BOOK 


Written  Exercise 
114.    Find  the  product  without  reducing  to  an 


improper  fraction : 

1.    15  times  7f . 

Process 

H 

Explanation 

15 

10 

105 

115   Ans. 

15x|=   10 

15  X  7  =  105 

15  X  7|  =  115 

2.   6|  times  18. 

Pkocess 

18 

Explanation 

108 

1 
6 

6f 

X  18  =  ^4-=   13J 
xl8=          108 
X  18  =          121J 

121| 


Written  Exercise 
115.    Find  the  products  :    , 

2. 
5 

7.    6fxl5  8 

10.   371x331x161  11 

X2.   1078x30f  x8j^x203^ 


1.  161x24 
4.   781x9 


731x35 
97|xl2 
83^x24 


3.   7261x8 
6.   987fxl5 
9.   401x60 
121 X  125|  X  20| 


COMMON  FRACTIONS  79 


In  the  multiplication  of  mixed  numbers,  it 
is  usually  the  best  plan  to  reduce  the  mixed 
numbers  to  improper  fractions.  Then  multiply, 
canceling  wherever  possible. 


To  Divide  a  Fraction  by  an  Integer 

116.   1.   Divide  |  by  3. 

Process  Explanation 

i-^3=i  jof|  =  i 

2.   Divide  |^  by  5. 

Process 
1     f;  _  1    4^  1  Explanation 

"2  "^  2"  ^     5" 

=  l.x4  iof  J  =  |times  J 


2  ^F 

~  10 

3.  In   the   exercise,   |-^3,  tell   how  to   obtain 
the  answer. 

4.  Give  the  answers  : 

2.^2  A-^4  -S^-^4 

10^5  10^2  ^-^3 

•   11  •  ^  11  •  ^  7    •  ^ 

5.  In  the  exercise,  J  -s-  5,  tell  how  to  obtain  the 
answer. 


To  divide  a  fraction  by  an  integer,  divide  the 
numerator  of  the  fraction  by  the  integer,  or 
multiply  the  denominator  of  the  fraction  by 
the  integer. 


80  INTERMEDIATE  BOOK 

In  dividing  ^^-  by  4,  we  may  multiply  the  de- 
nominator by  4  and  get  ^f ,  or  we  may  divide  the 
numerator  by  4  and  obtain  |.  Which  is  the  better 
way  ?     Why  ? 

In  dividing  |  by  4,  which  is  the  better  way? 
Why? 

Oral  Problems 

117.  1.  A  mother  divides  J  of  a  cake  equally 
among  3  children.  What  portion  of  the  whole 
cake  does  each  receive  ? 

2.  Mary  cuts  J  of  a  yard  of  ribbon  into  2  equal 
parts.     How  long  is  each  part? 

3.  Three  boys  are  given  f  of  a  pound  of  dates. 
How  much  is  each  boy's  share? 

4.  Four  baskets  of   coal  weigh  ^  of  a   ton. 
What  is  the  weight  of  1  basket  ? 

5.  John  jumps  ^  yd.  in  3  jumps.    What  is  the 
distance  covered  in  one  jump  ? 


Oral  Exercise 

118.   Answer  at  sight : 

1.   1  +  2 

2.  1  +  3 

3.  1  +  2 

4. 

1+3 

5.   J-*- 3 

6.1  +  2 

7.  i  +  3 

8. 

*-4 

9.    i  +  3 

10.  f  +  2 

11.  1  +  3 

12. 

1-4 

13.     1+3 

14.  1  +  6 

15.  1  +  4 

16. 

f-4 

17.     ^^2 

18.  ^3^  +  3 

19.   1*-+ 7 

20. 

¥-11 

COMMON  FRACTIONS  81 


Written  Exercise 

119.   Solve: 

1.   |l■^12 

2.    II   :  14 

3.  e^i5 

4.   ^^96 

5.  3V_^48 

6.  It -^21 

7.   11^24 

8.  e^i4 

9.  i^sji^3o 

10-   Wxfl^ 

•24 

11. 

125 

xi|-x|-^3 

To  Divide  a  Mixed  Number  by  an  Integer 

120.  Divide: 

1.    5iby3. 
Process 

^1  .  Q_26      Q  Explanation.  —  Reduce  the  mixed 

^  *          /ft      1  number  to  an  improper  fraction. 

=  "5"  ><  3  2^^  3  is  the  same  as  J  of  ^^-. 

=  ff  Solve  4  of -\^. 

2.  3|^5  3.  171-^13  4.  251^19 
5.  12|^5  6.  29|-^9  7.  49|-^17 
8.  6833^-^21    9.  791^18    10.481-^39 

To  Divide  an  Integer  by  a  Fraction 

Oral  Exercise 

121.  1.  Draw  a  line  4  in.  long.  Divide  it  into 
parts,  each  J  in.  long.  How  many  parts  are  there  ? 
How  many  fourths  in  1  ?     In  4  ? 

2.    4-^l  =  ? 


82  INTERMEDIATE  BOOK 

3.  Draw  a  line  6  in.  long.  Divide  it  into  parts 
each  ^  in.  long.  How  many  are  there  ?  How 
many  halves  in  1  ?     In  6  ? 

4.  6  +  1  =  ? 

5.  Draw  a  line  2  in.  long  and  divide  it  into  parts 
each  ^  in.  long.     How  many  parts  are  there  ? 

6.  2  +  i=? 

7.  Would  there  be  less  parts  if  the  divisor  were 

V 

8.  Tell  how  to  divide  an  integer  by  a  fraction. 


To  divide  an  integer  by  a  fraction,  invert  the 
fraction  and  then  multiply. 

Written  Exercise 

122.   Divide 

: 

1.    6byf 

• 

Process 

6H-|=6xf 

=  ¥ 

=  6f 

Explanation.  — 

Multiply. 

[nvert  the  divisor  -J. 

2.    9ft.  +  | 

3.  $6^$| 

4.5+1 

5.   8yd.-f-f 

6.  75mi. -^f 

7.  98  1b. +  1 

8.    128  +  1 

9.  200-^3-33- 

10.  1000  +  1 

11.   400  +  1 

12.  2000-^1 

13.  5000 +  f 

COMMON  FRACTIONS 


83 


To  Divide  a  Fraction  by  a  Fraction 
123.    Divide: 
1.   ibyf. 
Process 


2*3        2 

=  3 

4 


3 


Explanation.  —  Invert  the  divisor 
and  multiply. 


i)T 


2. 
14 


^■m 


2J3 
3/5 


4/2 


lU 


7)    7 


12 


11. 


15. 


1)4 

2/5 


i)^ 


8     l)-2- 
».    2^4 


12-    1)1 


16.   4)1 


5. 
9. 


4^3 

ivT 


13.  4:)i 


17. 


5)i 


To  divide  an  integer  or  a  fraction  by  a  fraction, 
invert  the  terms  of  the  divisor  and  proceed  as 
in  multiplication  of  fractions. 


To  Divide  an  Integer  by  a  Mixed  Number 


124.   Divide: 

1.    12by2|. 

Peocess 

12^21=12^1 

2 
2.   12  by  31 
5.  '69  by  30| 
8.   100  by  41| 

Explanation.  — 
mixed    number    to 
fraction.     Divide. 

Reduce     the 
an    improper 

3.  25  by  61         4. 
6.  84  by  42|       7. 
9.  600  by  84|    lo. 

49  by  51 
76  by  12f 
1000  by  961 

84  INTERMEDIATE  BOOK 

To  Divide  a  Mixed  Number  by  a  Mixed  Number 
125.   Divide: 


1.    Ill  by  81 
Process 

2 


Explanation.  —  Reduce 


2  X  ^4     4    ^^^  mixed  numbers  to  improper 
11 J  -5-  8^  =         ^^  =  —    fractions  and  divide. 
yL/  X  o      o 

2.  7f  by  2|   3.  41  by  3L    4.  21  by  3?- 
5.  4|  by  5|   6.  7^^  by  14f   7.  12f  by  16f 
8.  5|  by  251  9.  24|  by  IQi  lo.  lOQi  by  50i 

Written  Problems 

126.  1.  How  many  caps  can  be  purchased  with 
$  21,  if  each  cap  costs  $1? 

2.  If  a  book  costs  $  2,  how  many  books  can  you 
buy  with  $4?  If  a  book  costs  $f,  how  many 
books  can  you  buy  with  $  2  ? 

3.  Mrs.  Jones  spent  $  18  for  ribbon,  paying  $  |- 
a  yard.     How  many  yards  did  she  buy? 

4.  How  many  yards  of  lace  can  be  bought  for 
$25  at  $1  a  yard? 

5.  If  it  takes  f  lb.  of  flour  for  each  loaf  of 
bread,  how  many  loaves  can  be  made  from  one 
barrel  of  flour  weighing  195  lb.  ? 

6.  Mary  uses  f  lb.  of  sugar  for  a  cake.  How 
many  cakes  will  27  lb.  of  sugar  make  ? 


COMMON  FRACTIONS  85 

7.  In  a  sclioolroom  |  of  a  box  of  chalk  is  used 
each  school  day.  How  many  days  will  9  boxes 
last? 

8.  A  bootblack  uses  J^  of  a  box  of  blacking 
for  three  pairs  of  shoes.  How  many  pairs  can  he 
black  with  3  boxes  ?  How  many  boxes  does  he 
need  for  60  pairs  of  shoes  ? 

9.  If  21  yd.  of  cloth  are  needed  for  a  coat,  how 
many  coats  can  be  made  from  35  yd.  ?  How  many 
yards  are  needed  for  12  coats? 

10.  During  the  month  of  July  a  laborer  was  idle 
^  of  the  time.     How  many  days  was  he  idle  ? 

11.  At  $  2 J  per  volume,  how  many  books  can  be 
bought  for  $  18  ? 

12.  Find  the  cost  of  37  electric  globes  at  $^ 
apiece.     How  many  globes  can  be  purchased  for  $  5  ? 

13.  A  certain  postage  stamp  is  -|  in.  by  f  in. 
Give  its  area.  How  many  stamps  of  this  size  will 
it  take  to  cover  completely  a  page  7  in.  by  6  in.  ? 

14.  If  5  bu.  of  wheat  cost  $3|-,  what  is  the 
cost  of  1  bu.  ? 

15.  If  6  boys  earn  $  1^  in  1  hr.,  what  part  of  a 
dollar  does  each  earn  ? 

16.  Charles  has  $  2J.  How  many  railroad 
tickets  at  $J  each  can  he  purchase? 

17.  What  is  the  cost  of  21  books  at  $^  each? 

18.  What  is  the  cost  of  one  pencil,  if  6  cost  25)^  ? 


86  INTERMEDIATE  BOOK 

19.  If  one  electric  globe  costs  $J,  how  many 
dollars  will  7  globes  cost? 

20.  How  many  electric  globes,  at  $  J  apiece,  can 
be  bought  for  $2f  ? 

21.  How  many  pencils,  at  3^^  apiece,  can  be 
purchased  f or  7  ^  ?     For  21  ^  ? 

22.  What  is  the  cost  of  8  pencils  at  3^^  apiece  ? 

23.  Mary  buys  6  notebooks  and  pays  50^. 
What  is  the  price  of  each  ? 

24.  At  2^j^  apiece,  what  is  the  cost  of  5  lemons  ? 

25.  How  many  lemons,  at  2^^  apiece,  can  be 
bought  for  20^  ? 

26.  How  many  sheets  of  paper,  at  ^^  a  sheet, 
can  you  get  for  11^  ? 

27.  How  many  sticks,  |  yd.  long,  can  you  saw 
from  a  pole  2  yd.  in  length  ?  Draw  a  diagram  of 
the  pole  and  show  the  points  of  division. 

28.  A  peddler  has  17f  pecks  of  peanuts.  How 
many  times  can  he  fill  a  measure  that  holds  J  of 
a  peck  ? 

29.  How  many  tons  of  coal,  at  $  5 J  a  ton,  can 
be  bought  for  $57.75? 

30.  If  it  takes  20|-  yd.  of  canvas  to  make  a  tent, 
how  many  yards  are  needed  for  7  tents  ? 

31.  If  f  of  a  sack  of  flour  will  last  a  family 
1  week,  how  many  weeks  will  Gf  sacks  last  the 
family  ? 


REVIEW 
Written  Exercise 

127.   1.    Multiply  each  of  the  following  by  1^: 
22,  46,  50,  48,  64,  68. 

2.   Divide  each  of  the  following  by  |:  76,  66, 
84,  140,  126,  114. 


3.    Reduce  to  mixed  numbers :  -y^,  J-f  1,  -y-, 


125 


493     15  0 
11  '     12  • 


4.  Change  to  improper  fractions:  1^,  211,  31^ 
131    942.  751 

-*-^5?  "^^3?    *^2- 

5.  Which  is  larger,  l|l  or  421  ? 

6.  Multiply  each  of  the  following  by  12  :  211, 
31  61,  lOf,  25|,  111 

7.  Divide  each  of  the  following  by  6 :  S^,  8 J, 
71,  211  14i,  6|. 

8.  Perform  the  following  operations:  2^-^5|■, 
"2  •  ^4?  -"-8  •  4'  8  •    4  • 

Find  the  cost  of : 

9.  21  lb.  of  cheese  at  15^  a  pound. 

10.  2^  gal.  of  molasses  at  50^  a  gallon. 

11.  7:1^  lb.  of  coffee  at  40^  a  pound. 

12.  4|  yd.  of  ribbon  at  20^  a  yard. 

13.  24  shovels  at  $  f  each. 

87 


88  INTERMEDIATE  BOOK 

14.  5  tons  of  coal  at  $  S^-  a  ton. 

15.  IJ  bu.  of  apples  at  If  a  bushel. 

16.  lOJ-  A.  of  land  at  $200  an  acre. 

Tell  the  quantity  of  goods  purchased : 

17.  $  1^  worth  of  vinegar  at  $  J  a  gallon. 

18.  51  j^  worth  of  berries  at  S^^  a  quart. 

19.  85 j^  worth  of  milk  at  8J^  a  quart. 

20.  Lard  at  12^^  a  pound,  and  pay  $  1. 

21.  Butter  at  20^i^  a  pound,  and  pay  63^. 

22.  Candy  at  60^  a  pound,  and  pay  15^. 

23.  Tomatoes  at  16|^  a  can,  and  pay  50^. 

24.  Oranges  at  45j^  a  dozen,  and  pay  $1.35. 

25.  Silk  at  $  2J  a  yard,  and  pay  $  IJ. 

Problems 

128.  1.  An  envelope  is  6 J  in.  by  3^  in.  How 
much  greater  is  the  length  than  the  width  ?  Find 
the  perimeter. 

2.  A  wagon  and  its  load  of  coal  weigh  3^  tons. 
The  empty  wagon  weighs  |-  ton.  Find  the  weight 
of  the  coal. 

3.  A  ranchman  sells  f  of  his  corn  crop  and  then 
J  of  it.     What  part  has  he  left  ? 

4.  Find  the  perimeter  of  an  envelope  7^  in. 
long  and  5  in.  wide.  What  is  its  area  in  square 
inches  ? 


REVIEW  89 

5.  John  buys  ^  lb.  of  cheese  and  gives  ^  of  it 
to  James.     What  part  of  a  pound  does  James  get  ? 

6.  If  a  boy  sells  f  and  ^  of  his  marbles,  what 
part  has  he  left  ? 

7.  Draw  a  figure  and  show  that  f  of  |  an  inch 
is  f  of  an  inch. 

8.  A   carpenter   cuts   board,   f   ft.   long,   into 
pieces  J  ft.  long.     How  many  pieces  does  it  make  ? 

9.  If  a  boy  earns  $f  a  day,  and  spends  $f  a 
day,  in  how  many  days  can  he  save  $  1  ? 

10.  Draw  a  figure  and  show  that  f  in.  divided 
by  J  in.  gives  2  as  the  answer. 

11.  It  took  Louise  f  of  an  hour  to  embroider 
2  leaves.  How  long  did  it  take  her  to  embroider 
lleaf? 

12.  George  picked  7  qt.  of  berries  and  sold  them 
for  $  ^.     What  did  he  get  for  each  quart  ? 

13.  Albert  earns  $  5^  a  week  for  6  weeks.  How 
much  does  he  earn? 

14.  James  has  If  lb.  of  candy  and  is  allowed  to 
eat  I  of  a  pound  a  day.  How  many  days  will  the 
candy  last? 

15.  If  2  tons  of  coal  cost  $  lOJ,  what  will  6  tons 
cost? 

16.  What  is  the  cost  of  7^  yd.  of  silk  at  $  IJ  a 
yard? 


90  INTERMEDIATE  BOOK 

17.  How  many  yards,  at  $  f  each,  can  you  buy 
for  $81? 

18.  How  many  times  larger  is  $25  than  $5? 
$123  than  $7? 

19.  What  must  you  multiply  1 J  by  to  obtain  7|  ? 

20.  If  James  earns  $  21  a  day,  how  many  days 
must  he  work  to  earn  $30? 

21.  By  what  must  you  divide  10-|-  to  obtain  7J? 

22.  A  traveler  spends  $  16 J  in  6 J  days.  How 
much  does  he  spend  each  day  ? 

23.  Find  the  cost  of  20|-  lb.  of  sugar  at  5|-j^  a 
pound. 

24.  The  length  of  a  fourpenny  nail  is  If  in.,  a 
sixpenny  nail  2  in.  If  4  nails,  2  of  each  kind, 
are  placed  in  a  line,  end  to  end,  how  long  a  line 
will  they  make? 

Oral  Exercise 

129.  1.  What  does  the  denominator  of  a  frac- 
tion indicate?     The  numerator? 

2.  Make  a  drawing  and  show  that  J  =  f . 

3.  Reduce  to  sixths: 

*     I     i     I     ^     H     If- 

4.  Reduce  to  eighths: 

i  i  i  li  2f  3J. 


REVIEW 


91 


5. 

Reduce  to  ninths: 

f              i               5 

14 

4f- 

6. 

Reduce  to  twelfths: 

lit* 

4 

li 

2|. 

7. 

Reduce  to  integers  or  mixed  numbers : 

¥      ¥      ¥      ¥ 

2  3 
4 

¥ 

fl> 

¥      ¥      ¥      ¥ 

¥ 

¥ 

M- 

8. 

Reduce  to  improper  fractions: 

131        121        15|         10 

* 

iif 

20f, 

501        601      1001        11 

i    . 

12f 

lOf 

9. 

Reduce  to  their  lowest  terms: 

A             12              12              6 

A 

A 

^% 

^'o            A           T6           A 

2 
16 

A 

.%■ 

Oral  Exercise 

130.   1.   Multiply  each  by  ^: 

4       t       f       f 

1 

f 

iV- 

2. 

Find  ^  of  each: 

1      i      i      1 

3. 

4 

i 

f 

3. 

How  much  is  ^  of  each : 

2      1      f      i 

4 
3" 

14 

24? 

4. 

Take  |- of  each: 

i          1           1           f 

f 

4 

i- 

5. 

Find  J  of  each: 

4          i         f          i 

t 

i 

1- 

How  much  is  f 

of  each: 

i       i       i 

1 

H 

^ 

1? 

Find  ^  of  each : 

f     1     1* 

7 

4i 

13 

i- 

Find  f  of  each: 

i    i     ^ 

-H 

A 

t's 

1- 

92  INTERMEDIATE  BOOK 

6. 

7. 

8. 


Oral  Exercise 

131.  1.   Divide  |  by  each  of  the  following: 

1  1  2  3  2  5.  5 

3  2  3  ¥  :S"  6  12- 

2.  Divide  f  by  each  of  the  following: 

t  3  2  3  3  ^  ^' 

3.  Divide  f  by  each  of  the  following : 

4        i        i        I         li         li- 

4.  Divide  f  by  each  of  the  following: 

I       f       *       t       f       il       tt- 

Oral  Problems 

132.  1.  A  grocer  sold  1^  dozen  eggs  to  one  per- 
son and  f  dozen  to  another.  How  many  dozen 
eggs  did  he  sell? 

2.  A  boy  spent  -^  oi  a,  dollar  for  paper  and  $  f 
for  an  arithmetic.  How  much  did  he  spend  for 
both? 

3.  A  man  goes  to  market  and  spends  f  of  his 
money  for  goods  and  -^  for  dinner.  What  part  of 
his  money  is  left? 


REVIEW  93 

4.  If  a  pound  of  tea  costs  J  a  dollar,  what  will 
1^  pounds  cost? 

5.  A  man  owned  f  of  a  farm  and  sold  ^  of  his 
share.     What  part  of  the  farm  did  he  sell? 

6.  Of  f  of  an  acre  of  land,  bordering  on  the 
Mississippi  River,  ^  was  washed  away.  What  part 
of  an  acre  was  washed  away? 

7.  A  clerk  has  IJ  months'  vacation,  |  of  which 
is  spent  in  Colorado.  How  long  was  he  in  Colorado? 

8.  A  piece  of  ribbon  3|-  ft.  long  is  divided  into 
strips  ^  ft.  long.     How  many  strips  are  there  ? 

9.  How  many  pieces  of  paper,  each  -|  in.  long, 
can  be  cut  from  a  paper  4  in.  long  ? 

10.  Letters  are  mailed  at  the  rate  of  2^  an 
ounce,  books  at  the  rate  of  ^^  an  ounce.  How 
much  more  expensive  is  letter  postage  than  book 
postage? 

11.  How  many  pounds  of  tea  can  be  purchased 
with  $  6  at  the  rate  of  $  |  a  pound  ? 

Written  Problems 

133.  1.  A  boy  earned  $3^  one  day,  $1  the  next 
day,  and  $  |  the  third  day.  How  much  did  he  earn 
in  the  3  days  ? 

2.  A  father  earns  $4|  a  day;  his  son  earns 
$  1|-  a  day.  How  much  more  does  the  father  earn 
in  a  day  than  his  son  ? 


94  INTERMEDIATE  BOOK 

3.  A  road  is  built  1^  mi.  along  level  ground, 
2f  mi.  along  rising  ground,  and  5^  mi.  along  ground 
sloping  downward.     How  long  is  the  entire  road  ? 

4.  During  three  days  the  sun  shone  9},  8|,  and 
7f  hr.,  respectively.  How  many  hours  of  sunshine 
were  there  in  all  ? 

5.  A  train  travels  12^  mi.  faster  per  hour  than 
a  steamboat.  How  many  miles  farther  than  the 
boat  does  the  train  travel  in  16  hr.  ? 

6.  A  flower  bed  is  40|-  ft.  long  and  5i  ft.  wide. 
How  many  square  feet  in  its  area  ? 

7.  A  farmer  sold  235f  lb.  of  maple  sugar  at 
17f  ^  a  pound.     How  much  did  he  receive  ? 

8.  A  room  is  15|  ft.  long  and  121  ft.  wide. 
What  is  the  cost  of  a  molding  extending  entirely 
around  it  at  5^^  a  foot  ? 

9.  A  ship  is  worth  $  100,000.  A  man  owns  -f^ 
of  it.  If  he  sells  |  of  his  share,  what  is  the  value 
of  what  he  still  owns  ? 

10.  How  many  yards  of  cloth  can  be  bought  for 
$140  at  $  If  a  yard? 

11.  What  is  the  price  of  hay,  when  5|  tons  are 
worth  $  69  ? 

Written  Exercise 

134.   Reduce  to  the  least  common  denominator  : 


REVIEW 


95 


Written  Exercise 
135.   Perform  the  operations  indicated  : 


1. 

l  +  ii+l=? 

2. 

10-2|-3f=? 

3. 

lf+lf-f=? 

4. 

llj-f  +  f=? 

5. 

101  +  111— T=? 

6. 

20|  +  7|-6i  =  ? 

7. 

2fxitxf 

8. 

61 X  16  X  2| 

9. 

144  X  8f  X 1 

10. 

Six  31x3^ 

11. 

SOxS^Vxi 

12. 

1x16^x3 

13. 

9f^4f 

14. 

If-A 

15. 

27f^l6f 

16. 

¥x|-ii 

17. 

14i^5| 

18. 

67501^33^ 

136. 


Drill  Device  —  Magic  Squares 


1 

f 

i 

i 

^ 

i 

4 

1 

1 

i 

A 

A 

i 

i 

i 

f 

i 

7 
6 

1 

i 

1 

1.  In  the  first  magic  square,  find  the  sum  of 
the  three  numbers  in  each  line,  each  column,  and 
each  diagonal. 

2.  Do  the  same  in  the  second  magic  square. 

3.  In  the  third  square,  fill  the  vacant  places,  so 
that  the  sum  of  the  three  digits  in  each  line, 
column,  and  diagonal  will  be  If. 


96  INTERMEDIATE  BOOK 

Suggestive  Questions 

137.  1.  A  man  pays  a  nickel  carfare  twice  a 
day.  How  can  you  find  the  fare  he  pays  in  a 
month  ? 

2.  If  you  know  a  man's  salary  per  month,  how 
can  you  find  his  yearly  salary  ? 

3.  If  you  know  the  number  of  days  in  each 
month,  how  can  you  find  the  number  of  days  in  a 
year? 

4.  Each  member  of  a  class  needs  a  new  pencil 
every  month.  How  can  you  find  the  number  of 
months  a  gross  of  pencils  will  last  ? 

5.  If  a  telegrapher  knows  the  number  of  words 
he  can  send  per  minute,  how  can  he  figure  the  time 
it  takes  him  to  send  a  given  number  of  words  ? 

6.  John  has  a  certain  amount  of  money.  If  he 
knows  the  cost  of  writing  tablets,  how  is  be  to  find 
how  many  tablets  he  can  buy  with  the  whole  of 
his  money  ? 

7.  A  merchant  sells  shoes  at  a  price  that  en- 
ables him  to  double  his  money.  How  can  we  find 
what  they  cost  him  per  dozen  pairs  of  shoes  ? 

8.  A  confectioner  has  a  number  of  pounds  of 
candy  which  he  wishes  to  put  up  into  boxes,  all 
of  the  same  size,  each  holding  a  given  fraction 
of  a  pound.  How  is  he  to  find  how  many  boxes 
to  order  for  the  candy? 


REVIEW  97 

9.  If  you  know  how  fast  a  train  travels,  how 
can  you  determine  the  time  it  takes  the  train  to  go 
a  given  distance? 

10.  If  you  know  how  much  a  plant  grows  in  a 
month,  how  can  you  find  the  average  amount  of 
growth  per  day? 

11.  If  James  can  read  a  certain  number  of  pages 
per  hour,  how  can  you  find  the  number  of  pages 
he  can  read  in  a  week,  when  he  reads  a  fixed  num- 
ber of  hours  each  day  ? 

12.  If  you  know  the  number  of  stories  in  a 
building  and  the  height  of  each  story,  how  can 
you  ascertain  the  height  of  the  building? 

Drill  Exercise 

138.   1.    Find  the  sums  of  the  three  fractions  in 
each  line,  each  column,  and  each 
diagonal. 

2.  Add  f  to  each  of  the  nine 
fractions.     Add  ^J  to  each. 

3.  Subtract  each  fraction  from 
1^.     From  2. 

4.  Multiply  together  the  pairs  of  fractions  in  the 
first  two  columns.  The  pairs  of  fractions  in  the 
last  two  columns. 

5.  Divide  each  fraction  in  the  first  line  by  the 
fraction  below. 


4 

i 

* 

i 

f 

f 

1 

f 

^ 

98  INTERMEDIATE  BOOK 

6.  Divide  each  fraction  in  the  second  line  by  the 
fraction  below. 

7.  Divide  each  fraction  in  the  first  column  by 
the  fraction  to  its  right. 

8.  Multiply  the  fractions  along  each  diagonal 

by  |. 

9.  Subtract  each  fraction  along  the  diagonals 
from  f . 

10.   Add  each  fraction  along  the  diagonals  to  1^. 


QUANTITY   AND    COST 
Written  Exercise 
139.   Find  the  quantity  and  cost : 

1.  2  bbl.  of  flour,  each  196  lb.,  @   $4.65  per 
barrel. 

2.  7  tubs  of  butter,  each  60  lb.,  @   27^^  per 
pound. 

3.  6  bbl.  of  pork,  each  285  lb.,  @   $8.50  per 
hundredweight. 

4.  241  lb.  boxes  of  apricots,  each  12  lb.,  @  9^^ 
per  pound. 

5.  6  boxes  of   dates,  each  301b.,  @  $2.25  per 
box. 

6.  75  bbl.  of  pork,  each  200  lb.,  @  5|^  a  pound. 

7.  125  bales  of  cotton,  each  4  tons,  @   8J^  a 
pound. 

8.  30  sacks  of  grain,  each  200  lb.,  @   80^  per 
hundredweight. 

9.  If  1  of  a  box  of  peaches  cost  45^,  what  is 
the  cost  of  a  whole  box? 

10.    If  I  of  a  barrel  holds  66f  gallons  of  pine 
tar,  how  many  gallons  will  the  barrel  hold? 

99 


100  INTERMEDIATE  BOOK 

Written  Problems 

140.  1.  If  Robert  can  solve  9  problems  in  half 
an  hour,  how  many  can  he  solve  in  IJ  hr.,  at  the 
same  rate? 

2.  How  many  miles  can  James  walk  in  3  hr.,  if 
he  walks  7  mi.  in  2  hr.? 

3.  John  paces  off  the  length  of  a  fence  and  finds 
it  to  be  36  paces.  If  3  of  his  steps  measure  8  ft., 
how  many  feet  long  is  the  fence? 

4.  If  5  lb.  of  apples  can  be  bought  for  15j^,  how 
many  pounds  can  be  bought  for  45^  ? 

5.  Josephine  reads  50  pages  of  history  in  3  hours 
or pages  in  27  hours. 

6.  If  two  boys  working  together,  at  the  same 
rate,  can  do  a  piece  of  work  in  7|-  hours,  in  what 
time  can  one  do  it? 

7.  If  a  certain  supply  of  provisions  lasts  2  men 
18  days,  how  long  will  it  last  9  men? 

8.  The  Atlantic  liner  Lusitania  went  from 
Queenstown  to  New  York  in  4  days  and  19.9  hours, 
at  an  average  speed  of  24  miles  an  hour.  How  far 
is  it  between  Queenstown  and  New  York  ? 

9.  The  Mauretania,  a  sister  ship,  attained  an 
average  speed  of  25.83  miles  an  hour.  How  much 
farther  will  she  travel  in  10  hours  than  the  Lu- 
sitania? 


QUANTITY  AND  COST  101 

10.  One   year  the   skating  record*  foi*  100   yd:'  ' 

was  11^  sec.  or yd.  per  second,  6|:' — '-r4'ft!  pfe^\i  i 

second. 

11.  The  skating  record  for  400  yd.  was  46^ 
sec.  or yd.  per  second  or ft.  per  second. 

12.  The  distance  of  880  yards  in  skating  was 
made  in  1  minute,  36  seconds.  How  many  yards 
per  second  is  this? 

13.  In  the  year  1903  the  United  States  pro- 
duced 234,000  tons  of  cane  sugar  and  214,825  tons 
of  beet  sugar.  In  1906  it  produced  243,000  tons 
of  cane  sugar  and  431,796  tons  of  beet  sugar.  By 
how  many  tons  did  the  increase  in  the  production 
of  beet  sugar  exceed  the  increase  in  the  production 
of  cane  sugar? 

14.  Colorado  produced  2974  million  pounds  of 
beets  in  one  year,  from  which  334  million  pounds 
of  sugar  were  manufactured.  How  many  pounds 
of  beets  did  it  take  to  yield  one  pound  of  sugar? 

15.  A  merchant  buys  10  doz.  pairs  of  shoes  for 
$  360  and  sells  them  at  $  4  a  pair.  What  is  his 
profit? 

16.  A  grocer  buys  20  doz.  eggs  for  $  .25  a  dozen 
and  sells  them  at  $  .35  a  dozen.  How  much  does 
he  gain? 

17.  If  6  doz.  oranges  cost  $2.40,  what  will  1 
doz.  cost?     5  doz.  ? 


102  INTERMEDIATE  BOOK 

18.  A  dealer  buys  knives  at  $  .35  and  sells  them 
;»i  $:.50.     Y^^hat  is  his  profit  on  100  knives? 

19.  Find  the  cost  of  10  lb.  of  butter  at  $i  a 
pound. 

20.  Find  the  cost  of  5^  lb.  of  butter  at  $  J  a  pound. 

21.  What  is  the  value  of  2^  acres  of  land  at  $  1 8 
an  acre  ? 

22.  A  carpenter  earns  $.45  in  |-  of  an  hour. 
How  much  does  he  earn  in  an  hour  ? 

23.  Only  f  of  a  class  are  present.  If  30  are 
present,  how  large  is  the  class  ? 

24.  If  ^  of  a  flock  of  sheep  are  100  sheep,  how 
many  sheep  in  the  entire  flock  ? 

25.  f  of  the  distance  between  two  cities  is  27 
mi.     What  is  the  distance  ? 

26.  The  distance  between  two  towns  is  55  mi. 
How  much  is  |-  of  that  distance  ? 

27.  A  train  runs  35  miles  in  f  of  an  hour.  What 
is  the  rate  per  hour  ? 

28.  James  buys  10  tons  of  soft  coal  and  pays 
$  6 2 J.  What  is  the  cost  per  ton  ?  (Use  business 
fractions.) 

29.  What  is  the  cost  of  16  notebooks  at  $.12| 
apiece  ?     (Use  business  fractions.) 

30.  Find  the  cost  of  24  doz.  eggs  at  $.37^^  a 
dozen. 


QUANTITY  AND  COST  103 

31.  How  much  must  you  pay  for  40  yd.  of  cloth 
at  $.371  a  yard? 

32.  A  merchant  buys  1000  yd.  of  lining  at  $  .03 
a  yard  and  sells  at  $  .05  a  yard.     Find  the  profit. 

33.  A  real  estate  man  buys  a  lot  for  $  1,200.  He 
divides  it  up  into  3  small  lots  and  sells  each  lot  for 
$  600.     How  much  does  he  make  ? 

34.  Another  real  estate  man  buys  a  lot  for  $  2,500, 
pays  $  100  taxes,  and  then  sells  it  for  $  2,750.  How 
much  does  he  gain  ? 

35.  At  $  .08  a  pound  for  rice  and  $  .05  a  pound 
for  sugar,  how  much  will  10|-  lb.  of  each  cost  ? 

36.  A  woman  buys  3  boxes  of  starch  for  $  .50  and 
a  bag  of  flour  for  $  .75.  She  gives  the  clerk  a  $  5 
bill.     How  much  change  does  she  receive  ? 

37.  What  is  the  cost  of  15  hair  brooms  at  $  3.25 
each  and  3  mops  at  $  5.60  per  doz.  ? 

38.  A  business  house  orders  7  quartered-oak 
flat-top  desks  at  $  19.85  each  and  7  revolving  arm- 
chairs at  $  9.33  each.  What  is  the  total  cost  of 
this  order  ? 

39.  A  student  buys  3  books  at  $  1.25  each  and  a 
student's  notebook  for  37  cents.  He  gave  in  pay- 
ment a  $  10  bill.  How  much  change  should  he 
receive  ? 

40.  Find  the  cost  of  4^  yards  of  calico  at  6  cents 
a  yard;  5 J  yards  of  gingham  at  24  cents  a  yard. 


104 


INTERMEDIATE  BOOK 


Oral  Exercise  —  Cash  Register 

141.   This  picture  shows  a  cash  register.      If  a 
purchaser  pays  for  goods  amounting  to  $  3.45,  the 

Sri. 


A  Cash  Register 

clerk  presses  the  keys  marked  $3,40^,  and  5 ^.  This 
prints  the  amount  of  the  purchase  on  a  shp  of  paper 
within,  pushes  up  cards,  showing  the  purchaser 
the  sum  paid,  and  opens  the  cash  drawer. 

Suppose   the   purchaser   has   given  the  clerk  a 
$  5  bill.     The  clerk  puts  the  money  into  the  drawer. 


QUANTITY  AND  COST  105 

He  may  take  out  the  following  change :  a  5-cent 
piece,  a  50-cent  piece,  and  one  dollar.  He  hands  the 
change  to  the  customer,  in  the  same  order,  and  says, 
"  Three  fifty,  four,  five  dollars." 

1.  What  keys  must  be  pressed  to  indicate  the 
payment  of  each  of  the  following  sums:  $1.50, 
$1.46,  $2.35,  $4.75,  $3.05,  $2.14? 

2.  What  amount  of  money  is  shown  by  the  card 
register  when  the  following  keys  are  pressed : 

Dollars         Cents  Cbnts  Dollars         Cents  Cents 


1 

20 

5 

1 

60 

7 

2 

30 

6 

2 

90 

8 

3 

80 

5 

4 

10 

5 

3.  If  a  purchase  is  $  1.65  and  the  purchaser 
gives  the  clerk  $  2,  what  change  should  he  receive  ? 

4.  State  what  keys  the  clerk  must  press,  what 
coins  he  may  take  out  of  the  drawer,  and  what  he 
will  say  to  the  purchaser  in  each  of  the  following 
cases : 


AMoitnt 

Money  Given 

Amount 

Money  Given 

OF  Purchase 

IN  Payment 

op  Pxtrohase 

IN  Payment 

$1.75 

$2.00 

$3.85 

$4.00 

$2.55 

$3.00 

$1.97 

$2.00 

$2.95 

15.00 

$4.05 

$5.00 

5.  Let  some  of  the  pupils  of  the  class  act  as 
clerks,  while  other  pupils  make  supposed  purchases. 
Which  pupils  were  able  to  act  as  clerks  without 
making  mistakes  ? 


106  INTERMEDIATE  BOOK 

Written  Problems 
142.  Prices  of  Household  Goods 


Tea  Kettle 

$  .49 

Range 

$42.50 

Bread  Box 

.55 

Sideboard 

15.65 

Water  Bottle 

.23 

Refrigerator 

12.75 

Broom 

.15 

Kitchen  Table 

3.50 

Teapot 

.53 

Dining-room  Chair 

2.75 

Towels,  per  doz. 

2.15 

Kitchen  Chair 

1.25 

Oilcloth,  per  yd. 

.30 

Dining  Table 

24.65 

Linoleum,  per  yd. 

1.20 

China  Closet 

19.75 

1.  Mary  bought  a  tea  kettle,  a  water  bottle,  two 
brooms,  a  dozen  towels.  She  pays  her  bill  with  a 
$  5  bill.     How  much  change  does  she  receive  ? 

2.  Mr.  James  ordered  a  china  closet,  a  dining 
table,  a  kitchen  table,  and  a  range.  How  much 
was  his  bill  ? 

3.  Mrs.  Hathaway  has  $45.60  in  the  bank. 
How  much  does  she  lack  in  order  to  purchase  10 
yd.  of  linoleum,  2  doz.  towels,  a  dining-room  chair, 
a  sideboard,  and  a  china  closet  ? 

4.  Mother  sends  Martha  with  a  $10  bill  to  buy 
2  yd.  of  oilcloth,  a  kitchen  table,  a  teapot,  a 
bread  box,  and  a  kitchen  chair.  How  much  change 
should  she  bring  home  ? 

5.  Mr.  Newman  purchases  a  sideboard,  a  refrig- 
erator, a  dining  table,  and  a  bread  box.  He  has 
$  99.15  in  the  bank,  but  wishes  to  keep  at  least  $  50 
on  deposit  in  the  bank.  How  much  can  he  pay  on 
account  ? 


QUANTITY  AND  COST  107 

6.  Purchase  any  six  articles  you  like  and  find 
the  cost. 

7.  A  man  earns  $  100  a  month.  His  monthly 
expenses  are  $45.60.  Is  the  balance  sufficient  to 
pay  for  a  range,  a  kitchen  table,  two  dozen  towels, 
a  teakettle,  and  a  bread  box  ? 

8.  Mrs.  Grant  purchases  a  sideboard,  10  yd.  of 
linoleum,  3  brooms,  a  kitchen  table,  2  kitchen 
chairs,  a  refrigerator.  She  pays  $  30  on  account. 
How  much  did  she  have  charged  ? 

9.  Cash  sales  were  $  125.35  on  Monday,  $  130 
on  Tuesday,  $175.25  on  Wednesday,  $43.40  on 
Thursday,  $150.10  on  Friday,  and  $247.65  on 
Saturday.     How  much  were  the  sales  for  the  week  ? 

Drill  Device 

143.  At  the  completion  of  the  study  of  fractions 
use  the  drill  device.  Continue  the  drill  daily  for 
short  periods  of  rapid  accurate  work.  Vary  the 
numbers  to  be  added  and  subtracted  and  to  be  used 
as  multipliers  and  divisors.  Change  the  numbers 
on  the  drill. 

Speed  and  Accuracy 

Speed  and  accuracy  should  be  developed  in  the 
fundamental  operations.  Practice  should  be  con- 
tinued on  drills  of  this  kind,  in  fractions,  decimals, 
and  percentage  until  a  speed  of  about  60  correct 
answers  a  minute  can  be  obtained. 


108 


INTERMEDUTE  BOOK 


1 

1 

:^ 

^ 

^ 

\C0 

^ 

^ 

o 

(M 

"«* 

U5 

CD 

t> 

+ 

tH 

rH 

1 

1 

1 

o 

O 

O 

o 

o 

o 

o 

"5 

jj 

1 

1 

00 

t- 

?o 

lO 

Tf 

CO 

<M 

•1- 

1 

1 

1 

^ 

m 
^ 

7-i 

a 

^ 

to 

tH 

00 

^ 

s 

g 

rH 

o 

1— 1 

> 

1 

1 

^ 

P 

yA 

1 

1 

kJ 

s 

;^ 

cg\ 

;5^ 

::^ 

■^ 

CO 

(N 

p 

00 

o 

a 

rH 

tH 

rH 

iH 

I 

1 

1 

^ 

SCO 

;j^ 

:^ 

C^^ 

::)^ 

:;^ 

1 

(M 

(N 

»-H 

o 

(M 

r-\ 

rH 

iH 

rH 

1 

rH 

iH 

tH 

rH 

1 

1 

1 

SI 

SCO 

c^\ 

:^ 

^ 

^ 

^ 

+ 

1 

1 

1 

DECIMALS 
Review 

144.  Study  the  three  ways  of  writing  decimal 
fractions. 

1.  One  tenth 

2.  One  hundredth 

3.  One  thousandth 

4.  Five  tenths 

5.  Six  hundredths 

6.  Seven  thousandths 

7.  Twenty-five  hundredths 

8.  Seven  hundred  fifty- 

six  thousandths 

A  fraction  whose  denominator  is  10,  100,  1000, 
or  1  with  any  number  of  ciphers  annexed,  is  called 
a  decimal  or  a  decimal  fraction. 

A  decimal  fraction  may  be  written  in  three 
ways: 

In  words,  as,  one  tenth,  six  hundredths. 
As  a  common  fraction,  as,  ^,  yo^. 
By  using  the  decimal  point,  as,  .1,  .06,  756. 
Decimal    fractions    or    decimals   are   usually 
written  with  a  decimal  point. 

109 


A 

.1 

TUir 

.01 

1000 

.001 

A 

.5 

100 

.06 

iooo 

.007 

^^ 

.25 

1^ 

.756 

no 


INTERMEDLA.TE  BOOK 


145. 


Written  Exercise 
1.    Make  a  chart  like  the  illustration. 


Orders  of  Whole  Numbers  Orders  of  Decimals 

Millions  Thousands  Units  or  Ones  Thousandths 


M 

C 

O 
1 

i 

■D 
C 
3 

I 

(A 

C 

.2 

1 

c 
o 

h 

(A 

C 

o 

i 

tn 

-a 
c 
rt 
to 

3 
O 

x: 

■M 

■o 
d) 

•a 

c 

3 
I 

to 

■o 

c 

to 

■M 

c 
a> 

H- 

to 

c 
to 

3 
O 

x: 
h 

to 

■a 

c 

3 

to 

c 

to 

0} 

c 
O 

o 
to 

'E 

to 

i2 

to 

J= 

■!-« 

■D 

0) 

1- 
T3 

i 

I 

to 

x: 

■M 

■a 

c 
nJ 
to 

3 
O 

Sd  Period 

2d  Period 

1st  Period 

1st  Period 

4. 


5. 


2.  Count  the  orders  of  integers  shown  on  the  chart. 

3.  Count  the  orders  of  decimals. 
Name  the  orders  of  each. 
Write  on  the  chart  the  following  numbers : 
Four  and  five  tenths. 

Seven  and  six  tenths. 
Five  and  thirty-six  hundredths. 
Six  and  seven  hundredths. 
Ten  and  one  hundred  twenty-five  thousandths. 
In  these  numbers  and  indicates  the  position  of 
the  decimal  point. 


DECIMALS 


111 


Study  Exercise 

146.  1.  Into 
how  many  small 
squares  is  the 
large  square  di- 
vided? One  of 
the  smaller 
squares  is  ^fo 
of  the  large 
square.  Write 
this  as  a  deci- 
mal fraction. 


2.    How  many  of  these  smaller  squares  in  ^  of 
the  large  square  ? 


Then,  i 


100 


=  .50  =  .5. 


3.  In  I"  of  the  large  square  there  are small 

squares. 

Then,  i  =  ro"u-=  -^^  ^^  ^^®  large  square. 

4.  Shade   the   smaller   squares   which   together 
stand  for  ^  or  .07.     For  ^  or  .10  or  .1.     For 


M  or  .13. 


5.  The  entire  large  square  =  t  —  t  —  s"  =" T¥o* 

6.  Tell  from  the  drawing  J^o_  =  ^^  _2^  =  ^^,  ^ 


10* 


60 
107 


.75  =  h 

.  ?       80    __  ? 
■5"?  TOO"  — ■§" 


f^n  —     ?    _  ?  —  ?      20 

.OU  —  YolOr  —  4  "~  2'    lOTT 


?        40 
5"'    TOTJ" 


:§"? 


112  INTERMEDIATE  BOOK 

8.    Tell  from  the  illustration  what  decimal  frac- 
tions are  equal  to  the  following  common  fractions : 
1    1    1   _i_  _i      1      1 

2'  4'   5'  10?   20?  25'   50* 


FRACTIONS  TO   BE 

i=.25 
i=.75 

MEMORIZED 

Oral 

Exercise 

147.  1.  How  many  cents  in  $.5?  In  $.2?  In 
$.4?     Inf.l? 

2.  How  much  more  is  $  .5  than  $  .25? 

3.  How  much  more  is  $  .75  than  $.5? 
In  writing  money  $  .5  is  written  $  .50. 

4.  Mary  buys  candy  worth  $.35.  She  gives 
$J  to  the  clerk.  How  much  change  does  she 
receive  ? 

5.  A  matchbox  contains  100  matches.  One 
match  is  ^-^q  of  the  entire  number. 

6.  Frank  takes  |-  of  all  the   matches,   or  

matches. 

7.  Had  he  taken  only  J  of  all  the  matches,  he 

would  have  taken matches.     J  is  equal   to 

what  decimal  fraction  ? 


DECIMALS  113 

8.  Write  as  a  decimal  fraction  the  part  of  all 
the  matches  you  would  have  taken,  if  you  took  9 
matches.     11  matches.     37  matches. 

9.  Albert  had  100  old  five-cent  stamps  in  an 
envelope.  He  loses  .25  of  all  he  had.  How  many 
does  he  lose  ?     What  part  of  all  still  remains  ? 

10.  Henry  has  100  tin  soldiers.  He  gives  away 
^  of  them  to  George  and  J  of  them  to  James.  How 
many  has  he  left?     What  part  of  the  whole  is  this? 

Oral  Exercise 
148.   Read  97.58. 
There  are  two  ways  of  reading  97.58. 

(1)  Ninety-seven  and  fifty-eight  hundredths. 

(2)  Ninety-seven,  point,  ^ye,  eight. 

The  second  way  is  generally  preferred  because  it 
is  shorter. 

Read  1.4,  100.75,  45.05,  3.275,  005. 
Read  0.014,  7.09,  18.71,  19.1,  1.004. 
Write  in  the  form  of  decimal  fractions : 

3  3  5        1_1_    A_l_    A     7        f;  5  5       fi  8  7  .^ 

10?   100?   100'   -^10?  ^10?  ^100?  "100?  ^1000* 

Write  in  the  form  of  common  fractions : 
.3,  .13,  .05,  .75,  4.65,  3.03,  .575,  005,  1.006,  7.01, 
8.10,  10.101. 

Which  is  larger 

9.7  or  9.07?  9.86  or  9.68? 

5.8  or  8.5?  3.6  or  3.60? 
4.8  or  5.8  ?  4.320  or  4.32  ? 


114  INTERMEDIATE  BOOK 


Addition  of  Decimals 

.49.  Copy,  add, 

and  check : 

.  $     3.75 

2.  $735.15 

3.  $1095.64 

16.85 

176.45 

46.75 

195.43 

714.36 

9.49 

236.78 

895.85 

9864.25 

900.00 

100.25 

897.68 

736.45 

236.70 

1098.46 

$ 

$ 

$ 

In  adding  money,  the  decimal  points  are  put  in 
a  column  so  as  not  to  confuse  dollars  and  cents. 
Precisely  the  same  thing  is  done  in  adding  all 
decimal  fractions.  The  decimal  points  are  kept  in 
a  column.  Do  not  forget  to  write  the  decimal 
point  in  the  sum. 


101.13 

5.  973.1 

6.  796.125 

709.09 

79.175 

15.471 

1000.15 

100.65 

210.005 

793.75 

462.456 

75.6 

434.14 

75.5 

400.06 

11.25 

176.47 

750.005 

125.17 

55.125 

66.543 

Observe   the  groups   of    10  when  such  groups 
occur. 


DECIMALS  115 

7.    Copy   the  numbers  in   each  column.     Add 
vertically  and  horizontally : 

12.34  +   21.22  +916.       +567.8     = 

56.70  +232.4  +928.3     +     5.432  = 

88.90  +   25.26  +   89.76   +     4.678  = 

21.26  +272.8  +.     9.476+   48.65   = 


9. 


+           +           + 

= 

12.14   +     2.905+   99.15   + 

364.       = 

13.73   +     3.062+   88.25  + 

98.9     = 

16.27   +   31.35  +   77.5     + 

897.5     = 

17.85   +   33.35  +   66.25  + 

6.432  = 

18.05   +353.6     +     5.125  + 

78.23   = 

+               +               + 

= 

8.479  +  698.9     +795.3     + 

478.79   = 

584.7     +   89.67   +   93.57   +' 

r879  6     = 

49.76  +875.4     +     6.932  + 

43.715  = 

75.42   +196.8     +   58.75   + 

791.45   = 

66.53   +789.15   +     4.676  + 

89.176  = 

78.90   +  67.817  +  798.       + 

458.9     = 

634.5     +819.43   +       .95   + 

45.61   = 

4.571  +  278.9     +638.7     + 

79.05   = 

+  +  +  = 

10.  Copy  and  add  the  answers  to  7,  8,  and  9. 

11.  Separate  Ex.  9  into  two  parts.  Add  and  find 
the  sum  of  the  answers.  Compare  with  the  answer 
to  9. 


116  INTERMEDIATE  BOOK 

Subtraction  of  Decimals 

150.  Copy  and  subtract : 

I.  $10.75  2.    11.251b. 

9.28  7.45  lb. 

3.   119.45  yd.  4.  120.6  mi. 

73,15  yd.  14.75  mi. 

Since  6  tenths  are  equal  to  60  hundredths,  we 
may   write    120.60    in    place    of    120.6.       Then, 
120.60-14.75  =  105.85. 
5.    $419.1 -$296.7.        6.    $786.55 -$654.6. 
7.   786.4  T. -  6.98.7  T.    8.   1000  lb.- 736.45  lb. 
9.   Subtract  1.795  from  12.     lo.   2.364  from  5.7. 
Process  Process 

12.000  =  12.  5.700  =  5.7 

1.795=   1.795  2.364  =  2.364 

10.205  =  10.205  3.336  =  3.336 

How  do  you  check  subtraction  ? 

II.  Subtract  69.7895  from  79.123. 

Multiplication  of  Decimals 

Oral  Exercise 

151.  1.    If  a  boy  earns  $  1.25  a  day,  he  earns 
$  12.5  or  $  12.50  in  10  days,  and  $  125  in  100  days. 

In  multiplying  by  10,  move  the  decimal  point 


DECIMALS  117 

one  place  to  the  right.     How  do  we  multiply  by 
100?     By  1000? 

2.  Multiply  the  following  by  10.     Also  by  100  : 
$7.35,  7.75  T.,  95.5  lb.,  73.47  ft.,  .1  in.,  75  bu., 

$2,335,  791.9,  78.732  mi.,  .05  oz. 

3.  Multiply  35.2  by  200.     Multiply  by  2.   Then 
multiply  the  product  by  100. 

4.  Multiply  each  by  10.     Multiply  each  by  20 : 
1.11         3.4         4.33         3.23         10.2         10.24 

10.15        2.05       2.44         2.25  .25  .04 

5.  Multiply  each  by  100.     Multiply  each  by  300 : 
$  1.11       2.22  lb.      30.3  ft.      3.2  yd.       2.2  doz. 

10.5        1.05  3.23         2.21  lb.        .25 

6.  Multiply  each  by  10.     Multiply  each  by  40: 
$1.21         2.11         11.2  T.        10.2  yd.         4.1  pk. 

3.02         1.22  1.05  .25  .5 

Oral  Problems 
152.   1.   If  the  wages  of  each  man  in  a  factory 
employing  100  men  are  $  2.25,  what  is  the  amount 
of  the  payroll  for  one  day? 

2.  If  a  train  goes  .75  mile  a  minute,  how  far 
will  it  go  in  100  minutes?     In  200  minutes? 

3.  A  boy  walks  112.5  yards  per  minute.      How 
many  yards  in  10  minutes? 


118  INTERMEDIATE  BOOK 

To  Multiply  a  Decimal  by  an  Integer  or  an  Integer 
by  a  Decimal 

153.   1.   Multiply  .75  by  9. 

Process        Explanation.  —  If  we  were  multiplying 
.75      75  by  9,  the  product  would  be  675. 
9  But  we  are  multiplying  -^  by  9.     Hence 


5  75      the  product  is  |^,  or  6.75. 
2.    Multiply  64  by  .8. 

Process        Explanation.  —  If  we  were  multiplying 
64      64  by  8,  the  product  would  be  512. 
.8  But  we  are  multiplying  64  by  -^.    Hence 

51.2      the  product  is  ^^-^-,  or  51.2. 


TO  MULTIPLY  A  DECIMAL  BY  A  WHOLE  NUMBER 

I.    Multiply  as  in  whole  numbers. 
II.    Point  off  as  many  decimal  places  in  the 
product   as   there   are    decimal    places    in   the 
multiplier. 


Written  Exercise 

154.    Multiply: 

1.  .15  by  8  2.  .25  by  9 

3.  .09  by  15  4.  3  by  $1.15 

5.  13  by  $2.25  6.  11  by  .95 

7.  12  by  10.5  8.  21.75  ft.  by  29 

9.  2579  lb.  by  .87  lo.  458  by  .009 

11.  .043  by  798  12.  457987  by  .0009 


DECIMALS 


119 


Written  Exercise 

155.   Multiply  each  number  in  columns  B,  C,  D, 
and  U,  by  the  corresponding  number  in  column  A. 


A 

B 

C 

D 

E 

1. 

19 

.62 

1.05 

10.36 

6.45 

2. 

109 

.705 

8.25 

19.75 

14.95 

3. 

28 

.901 

9.28 

109.6 

121.5 

4. 

307 

.025 

7.01 

203.5 

906.7 

5. 

412 

.909 

8.75 

100.9 

976.5 

6. 

505 

.097 

1.89 

23.45 

8.756 

7. 

620 

.202 

3.333 

89.01 

45.67 

8. 

136 

1.012 

.963 

75.75 

UA4: 

9. 

809 

8.97 

7.09 

45.45 

67.5 

10. 

879 

.009 

.008 

.007 

.006 

To  Multiply  a  Decimal  by  a  Decimal 
156.   1.    Multiply  .64  by  .8. 

Process  and  Explanation 

If  we  were  multiplying  64  by  8,  the  product 
would  be  512. 

But  we  are  multiplying  -^^  by  ^ . 
Hence  the  product  is  yu^,  or  .512. 

2.   Multiply  4.28  by  1.15. 

Process  and  Explanation 
If  we  were  multiplying  428  by  115,  the  product 
would  be  49,220. 


120  INTERMEDIATE  BOOK 

But  we  are  multiplying  ^f|-  by  ^^. 

The  product  is  ^Uih  or  4.9220,  or  4.922. 


TO   MULTIPLY  A  DECIMAL  BY  A  DECIMAL 

I.    Multiply  as  in  whole  numbers. 
II.   Point  off  as  many  decimal  places  in  the 
product  as  there  are   decimal   places   in  both 
factors. 


Oral  Exercise 

157 

.   Answer  at  sight 

1. 

.9x.2 

2. 

.8x.3 

3. 

.6x.4 

4. 

.5x.5 

5. 

.4x.7 

6. 

.3x8 

7. 

.2x.8 

8. 

10  X. 8 

9. 

10  X. 3 

10. 

.4x10 

11. 

1.1  X  .2 

12. 

1.2  X. 3 

13. 

.4x2.1 

14. 

.5x1.2 

15. 

3x3.1 

16. 

.3  X  3.1 

17. 

.5x1.1 

18. 

5x.ll 

19. 

.llx.l 

20. 

.17x2 

21. 

.2  of  .4 

22. 

.4  of  .8 

23. 

1.1  of  .9 

24. 

7  of  .12 

25. 

12x12 

26. 

1.2x12 

27. 

1.2x1,2 

28. 

1.2  X. 12 

29. 

1.1x12 

30. 

11x1.2 

31. 

1.1  X. 12 

32. 

.llx.l2 

33. 

13x11 

34. 

13x1.1. 

35. 

13  X  .11 

36. 

1.3  X. 11 

Written  Exercise 

158.   1.   Find  the  product  of  195  and  32.     Also 
of  19.5  and  3.2. 


DECIMALS  121 

2.    Which  of  the  three  products  is  the  largest : 
1.2x1.8,  12x18,  .12x1.8? 


Multiply  : 

3. 

2.5  X  3.2 

4. 

6.7x7.5 

5. 

77.7x6.6 

6. 

6.3x8.5 

7. 

9.8x1.2 

8. 

37.5  X. 05 

9. 

16.5x12.9 

10. 

3.5x2.06 

11. 

1.07  X. 35 

12. 

.01 X. 5 

13. 

19.1  X. 01 

14. 

.05  X  .96 

15. 

.7  of  35.6 

16. 

1.25  X. 7 

17. 

.1x7.5 

18. 

7x6.8 

19. 

.9  of  10.7 

20. 

12.5  X. 85 

21. 

.2  of  7.3 

22. 

7x6.8 

23. 

.6  of  11.3 

24. 

9.17  X. 65 

25. 

.3  of  9.4 

26. 

91x87 

27. 

.05  of  9.8 

28. 

8.06  X. 54 

29. 

.03  of  8.5 

30. 

9.1x8.7 

31. 

.15  of  125 

32. 

0.25  X  .25 

33. 

.33  of  6.1 

34. 

.64X.75 

35. 

92.34x81.4 

36. 

80.43  x  76.4 

37. 

764.1x17.9 

38. 

63.01x70.6 

39. 

19.84x1.25 

40. 

670.9x15.2 

41. 

99.9x8.88 

Written  Problems 

159.  1.  The  wheat  yield  of  a  field  of  19.6  acres 
is  at  the  rate  of  27.5  bushels  per  acre.  What  is 
its  value  at  $  1  a  bushel  ? 

2.  If  1  ft.  of  lead  piping  weighs  1.82  lb.,  what 
is  the  weight  of  a  piece  of  piping  22.5  ft.  long  ? 

3.  If  an  aeroplane  travels  at  the  rate  of  67.5  mi. 
an  hour,  how  far  will  it  travel  in  3.4  hr.  ? 


122  INTERMEDIATE  BOOK 

4.  At  25.3  mi.  per  hour,  how  far  can  you  ride 
in  4.5  hr.? 

5.  A  carpenter  earns  $  4.25  a  day.  How  many 
days  will  he  have  to  work  in  order  to  earn  $  180  ? 

6.  A  farm  consists  of  120  acres.  It  is  valued 
at  $  7500.50.     What  is  the  value  per  acre  ? 

7.  To  find  the  diameter  of  a  circle,  divide  the 
length  of  the  circle  by  3.1416.  What  is  the  diam- 
eter of  a  circle,  if  its  length  is  25  ft.  ? 

8.  What  is  the  diameter  of  a  circle,  if  its  length 
is  50  ft.  ? 

Division  of  Decimals 

To  Divide  Integers  and  Decimals  by  Integers 

160.  1.  20  divided  by  5  may  be  written  5)20, 
2/-,  or  20-^-5. 


2.    Since  1.56  x  10  =  15.6,  we  have  10)15.6  =  ? 


3.    Since  1.565  x  100  =  156.5,  we  have  100)156.5 


TO  DIVIDE  A  NUMBER  BY   10 

Move  the  decimal  point  in  the  dividend  one 
place  to  the  left. 

In  multiplying  by  10,  the  decimal  point  is 
moved  one  place  to  the  right. 

In  dividing  by  10,  the  decimal  point  is  moved 
one  place  to  the  left. 


DECIMALS  123 

4.    Tell  how  to  divide  a  number  by    100.     By 
1000. 

Written  Exercise 

161.   1.   Divide  222.4  by  200. 

Divide  222.4  by  100,  and  the  result  by  2. 

1.112 


100)222.4  =  2.224,  2)2.224 


2.    10)35.4         100)35.4 


3.   100)5.6         20)4.4 


4.    100)115.6     100)22.2 


5.   10)55.5        50)55.5 


10)3.7 

100)3.7 

20)44 

20).44 

200)22.2 

200)222 

30)36.3 

40)4.8 

6.  90)3600   400)3200  300)7200  30)60.6 

Written  Exercise 

162.   1.   Divide  427.2  by  24. 

Process 

17  8 

X  Explanation.  —  Divide    as  in  whole 

24)427.2  numbers.     24  into  42  tens  goes  1  ten  and 

24  a  remainder.     Write  the  1  above  the  divi- 

YS7  dend  in  the  tens'  column  and  so  on.     Place 

-1  go  the  decimal  point  in  the  dividend  and  quo- 

1  Qo  tient  under  each  other. 

192 


124 


INTERMEDIATE  BOOK 


2.    13)1599 


5.   21)51.03 


3.   13)159.9 
6.   53)424 


8.    62)43.4 


9.    64)38.4 


11.    131)10.48     12.    139)834 


14.    17)212.5      15.    23)632.5 


17.   83)207.5      18.   39)48.75 


20.    17).85  21.   16)1.28 


4. 

X 

23)538.2 

7. 

58)5.22 

10. 

127)88.9 

13. 

151)120.8 

16. 

97)145.5 

19. 

76)588.84 

22. 

19). 57 

23.   19).285        24.    16).272  25.   14).182 


Written  Problems 

163.  1.  A  dozen  handkerchiefs  sell  for  $2.88. 
What  is  the  price  of  one  handkerchief  ? 

2.  Nine  boys  hire  rowboats  and  pay  $2.25. 
What  is  each  one's  share  of  the  expense  ? 

3.  On  a  football  trip  the  expense  of  13  men 
was  $  14.95.     How  much  did  each  pay  ? 

4.  If  the  fare  of  35  pupils  on  an  excursion  is 
$15.75,  what  is  the  fare  of  one  ? 

5.  A  town  in  Colorado  had  226.3  hr.  of  sun- 
shine during  a  month  of  31  da.  What  was  the 
daily  average  ? 

6.  A  potato  patch  contains  67.5  sq.  yd.  It  is  in 
the  form  of  a  rectangle  9  ft.  long.     How  wide  is  it  ? 


DECIMALS  125 

7.  A  white  ash,  29.9  in.  thick,  was  115  yr.  old. 
Find  the  average  yearly  growth. 

8.  A  tree  grows  to  a  height  of  77.9  ft.  in  41 
yr.  What  was  its  average  gain  in  height  per 
year? 

9.  A  train  travels  213.6  miles  in  6  hours. 
How  many  miles  is  this  an  hour  ? 

10.    In  a  long-distance  race  one  man  ran  24  miles 

in  2  hours,  57.6  minutes.     He  ran  1  mile  in 

minutes. 

To  Divide  a  Decimal  by  a  Decimal 

164.   1.    f  =  ?     ■§-§■  =  ?     Compare  the  quotients. 

«9._?  1_8— ?  2_7  —  ?  36  _? 

^.3  —  .  "e""-  9~*  12~* 

2.5      ?  3.6      ?  1.25      ? 


3. 


.5      5  .6      6  .05     5 


2  5  25        .      .         . 

Instead  of  — ^  we  may  take  — ,  which  is  easier 
.5  5 

to  divide. 

2.5     «       3.6     o       4.5     o       1.25 


4. 


.5      '         .6      '        .5      '        .05      * 


5.    1.5^.5       .25)775       .9)4.5         .9)6.3 


6.   .6)4.2         .7)5.6         .2)1.4         .7)2.1 
.45 


7.    -j=''       .8)7.2         .9)4.5         .6)7.2 


126  INTERMEDIATE  BOOK 


PRINCIPLE  TO  BE  REMEMBERED 

Multiplying  the  dividend  and  divisor  by  the 
same  number  does  not  change  the  quotient. 


Written  Exercise 
165.   Answer  the  following : 

1.    .6)91 


4.    .11)1.21 


7.    .8)6.4 


10.    1.2)1.44 
13.   25)75 


2. 

1.2)7.2 

5. 

.9).81 

8. 

.08).64 

11. 

12)1.44 

14. 

2.5)7.5 

3. 

1.1)1.21 

6. 

.09).81 

9. 

.12)1.44 

12. 

12)14.4 

15. 

2.5)75 

16.   2.5).75  17.   .12)1.32         is.    1.3)910 

Written  Exercise 
166.    Divide: 

1.    1.872  by  .13. 
Process 
14.4 

X 

13)187.2  Explanation.  —  The  divisor  becomes 

13  an  integer,  if  we  multiply  by  100.     We 

~57  have  .18)1.872  equal  to  13)187.2. 

52 
52 
52 


DECIMALS  127 

2.    77  by  2.5. 

Process 

3Q  g  Explanation.  — 770  -^  25  gives 

X  the  quotient  30  and  the  remainder 

25)770.0  20.     If  the  division  is  carried  one 

75  step   farther,    in    order    to    secure 

200  greater   accuracy,    then    write    the 

200  dividend  770.0  instead  of  770.   The 

next   digit   in   the   quotient    is   8. 

Check :  30.8  There  is  no  remainder.     The  exact 

2-5  quotient  is  30.8.     Check  by  multi- 

1540  plying  the  quotient  by  the  divisor. 

616  What  should  the  product  be  ? 


77.00 

3. 

224  by  2.4 

4. 

1718.64  by  .62 

5. 

$775  by  $.25 

6. 

74.256  by  .34 

7. 

$  8955  by  4.5 

8. 

10548.72  by  .39 

9. 

1718.64  by  9.3 

10. 

150.696  by  2.8 

11. 

6715.1756by.085 

12. 

566.351  by  6.7 

Written  Problems 

167.   1.    What  number,  multiplied  by  1.2,  gives 
the  product  14.4  ? 

2.  Multiplying  a  certain  number  by  1.3  yields 
the  product  11.7.     What  is  the  number? 

3.  The  product  is  $  10.35,  the  multiplier  is  2.3 ; 
what  is  the  multiplicand  ? 

4.  If  a  man  earns  $26.25  in  7.5  days,  how 
much  does  he  earn  in  one  day  ? 


128  INTERMEDIATE  BOOK 

5.  John  earns  $  3.60  a  week.  His  father  earns 
$  18  a  week.  How  many  times  greater  than  the 
son's  are  the  father's  wages  ? 

Written  Exercise 

168.  Divide,  carrying  the  quotient  to  3  decimal 
places. 

1.  9.2  by  1.3. 
Process 

7.076 

X  Explanation.  —  When  we  divide   92 

13)92.000  by  13,  there  will  always  be  a  remainder, 

91  however  far  we  carry  the  division.     When 

100  it  is  not  necessary  to  know  the  fractions 

91  of  a  cent,  we  write  the  answer,  $7.07'^. 

90  The  plus  sign  shows  that  the  quotient 

>To  7.07  is  not  exact  and  that  the  true  answer 

Y^  is  a  little  larger. 

2.  73-^2.9  3.    97^.41 
4.   107^5.3  5.   4.55 -^  9.7 

6.  2.55^1.07  7.   .75^8.9 

8.    $1.8^6.4  9.    7.95  in. -^12 

10.   272.5-4-2.72  ii.   7.63  lb. -^17 

Written  Problems 

169.  1.  The  area  of  a  drawing  board  is  483.5 
sq.  in.,  its  length  is  23.1  in.  Compute  its  width 
to  the  tenth  part  of  an  inch. 


DECIMALS  129 

2.  A  place  in  Arizona  had  305.4  hr.  of  sun- 
shine during  January.  What  is  the  daily  aver- 
age? 

3.  The  salary  of  the  President  of  the  United 
States  is  $  75,000.  What  is  his  salary  for  a  day 
in  a  year  of  365  days  ? 

4.  A  man  travels  1,896  miles  in  his  automobile 
during  the  month  of  July.  How  many  miles  a 
day  does  he  average  ? 

5.  During  March,  a  few  years  ago,  406.1  tons 
of  dynamite  were  used  for  blasting  the  Panama 
Canal.  On  an  average,  how  many  tons  of  dyna- 
mite were  used  a  day?  How  many  pounds  of 
dynamite  were  used  a  day  ? 

To  Change  a  Decimal  to  a  Common  Fraction 

170.   1.    Change  .625  to  a  common  fraction  in 
its  simplest  terms. 

Process  Explanation. — Write  in 

oi)n_   625  ^^^  form  of  a  common  frac- 

no«  ~,\^        .  tion.     Cancel.      What   com- 

125  —  25  —  5         Ario  ,     ,^ 

200-40-8      ^^^*-      mon  factors  were  canceled ? 

2.  .8        3.  25         4.  .75       5.  .125        6.  .64 

7.  .05      8.  .2  9.  .08      10.  .35        11.  .28 

12.  .95    13.  .96      14.  .55     15.  .175      i6.  .16 

17.  .48     18.  .225     19.  .175    20.  .125      21.  .725 


130  INTERMEDIATE  BOOK 

To  Change  a  Common  Fraction  to  a  Decimal 
171.   1.    Change  -|  to  a  decimal. 
Process 


3.— 
4 


^r  Explanation 


2.   Change  2^5  to  a  decimal. 

Process 

32  Explanation 


283  =  8^25  =  8.00^25  =  . 32  ^m 


25)8.00 

3.    Change  ^  to  a  decimal. 

Explanation.  — In  changing  J  to  a 
decimal,  we  find  that  the  division  does  not 
come  out  exact.     ^  cannot  be  exactly  ex- 

Process  pressed  as  a  decimal.  In  such  a  case  carry 
.SS"*"     the  answer  to  the  second  or  third  decimal 

3)1.00  place  by  adding  as  many  ciphers  to  the 
dividend  as  there  are  to  be  decimal  places 
in  the  answer.  Write  plus  after  the  last 
figure  in  the  quotient  to  show  the  omis- 
sion of  the  rest. 

Written  Exercise 
172.   Reduce  to  decimals  : 


i 

2. 

i 

3. 

¥ 

4. 

H 

5. 

H 

6. 

M 

H 

8. 

It 

9. 

« 

10. 

W 

11. 

H 

12. 

¥ 

i 

14. 

5 
6 

15. 

4 

T 

16. 

i 

17. 

7 
11 

18. 

18 
13 

7. 
13. 

In  examples  13-I8  carry  the  answer  out  to 
decimal  places. 


DECIMALS  131 


Written  Exercise 
173.   Reduce  to  mixed  numbers 

1.    -^Z  2.    y  3.     -W 


M  6.    fl  7.     H  8.    I 


10       3J_9_  n       10_0  T«       81 


8  1_5_  Trt       379  n        1 0_0 


174.    Reduce  to  a  decimal,  carrying  the  answer 
out  four  places : 


1.    ^i". 
Process 
10.4146- 


41)427.0000 

^2  Explanation.  —  Add    ciphers    in 

the   dividend   to    make    four    decimal 
places.     Indicate  the  first  partial  divi- 
dend. 
Divide : 


17  0 
16  4 


60 

41  Indicate  the  incomplete   answer   by 

190       the  +  sign. 

164 

260 

246 

2       573  3       648  a       8  2  9  5       9Jl6 


REVIEW 
Decimal  Fractions 

175.   1.   Eead:  .27,  3.01,  4.025,  .007,  .726. 

2.  In  .32,  the  unit  is  divided  into  equal 

parts,  and of  these  are  taken. 

3.  How  can  we  tell  the  denominator  of  a  frac- 
tion when  it  is  written  in  the  decimal  form  ? 

4.  Arrange   in   the   ascending  order  of  value: 
5.05,  5.51,  5.5,  5.005. 


Oral  Exercise 

176.   Add  at  sight : 

1.     3.2 

2.   7.8 

3.   3.7 

4. 

10.3 

4.5 

2.4 

4.8 

20.8 

5.    10.7 

6.     .07 

7.     .03 

8. 

6.44 

15.01 

.14 

.145 

1.4 

9.   2.07 

10.   7.01 

11.   9.09 

12. 

7.993 

.155 

2.10 

3.46 

1.007 

Oral  Exercise 

177.   Subtract  at  sight : 

1.     7.5 

2.   7.4 

3.   10.6 

4. 

7.5 

2.5 

2.5 

4.7 

1.05 

132 


REVIEW 

133 

8.7 

6.   9.7          7.       .100 

8. 

.200 

8.65 

7.9     ■              .001 

.005 

1.9 

10.   3.75       11.     7.111 

12. 

5.000 

.05 

1.7                 3.01 

.001 

Oral  Exercise 

178.  1.    Change  to  common  fractions  and  simpli- 

fy:   .4,  .8,  1.2,  .25,  .75,  .5,  .55 

2.  Change  to  decimal  fractions : 

1    i    1     3.     2.     3.    4 
5?  4?  2?  4?  5?  5?   5 

3.  Express  in  dollars  and  cents : 

$11  $11  $41  $lf,  $2f,  $3f 

Compare  and  determine  which  is  the  larger: 

71  and  7.2  8.5  and  8f 

7.4  and  7.40  4.4  and  4i 

3.3  and  31  2|  and  2.6 

Drill  Exercise 

179.  1.    Add  the  numbers  in  each  column. 

2.  Subtract  the  lesser  numbers  from  the  greater 
in  each  column. 

3.  Find    the  product  of  the  two  numbers  in 
each  exercise. 

4.  Divide  the  first  number  by  the  second. 

A  BCD 

1.1,  2.2 


1. 

hi 

^o>i 

.hi 

2. 

i-i 

.5,  .25 

i,l 

134  INTERMEDIATE  BOOK 


A 

B 

0 

X> 

3. 

H,  H 

2^1 

2J,i 

2i,i 

4. 

2,  .4 

.3,3 

%f 

hi 

5. 

hi 

l.i 

100'  -5 

•25,^ 

6. 

101  2 

%i 

3^,7 

31  .7 

7. 

31,  .1 

5i,f,r 

51,11 

2*4'  12 

8. 

A>i 

A>f 

I,2i 

hi 

9. 

hi 

f>f 

hi 

i.25 

10. 

.331  .661 

.75,  .25 

.5,  121 

.121  .25 

11. 

•161, 1 

|,-5 

f,  .661 

.75,1 

12. 

hi 

.99,2 

.49,1 

1,1 

13. 

.5,  .6 

4.5,2 

8.6,2 

1.2,3 

14. 

24,  .2 

36,  ^ 

3.6,  xk 

4.7,  .1 

15. 

H,H 

21,1 

1,  .01 

.9,  A 

16. 

.11,  .11 

.12,  .12 

.01,  .05 

1.3,  13 

17. 

H,H 

hi 

hi 

1    A 
4'  5 

18. 

hi 

1,  .33i 

200,  300 

250,  350 

19. 

2i,i 

hH 

TT'  to 

h"^ 

20. 

3^,1 

1.1,  .1 

2.2,  .2 

3.3,  .3 

Oral  Exercise 

180.    Find  the  product : 

1.    .7x.6              2.    12x1.2  3.  Tx.lll 

4.    8x1.2             5.    1.2x1.2  6.  .8x.l2 

7.    .Ix.l              8.    1.2x12  9.  8x1.2 

10.   .25x5           11.   .15x5  12.  .05x5 


REVIEW  135 

Oral  Exercise 

181.  Find  the  quotient : 

1.    .74-^10  2.    1.4-f-lO  3.    14-^10 

4.  62 -f- 100         5.    6.2-^100         6.   620 -^  100 
7.    14-f-.l  8.   1.5^.1  9.   2.03^.1 

10.   24-^.2  11.    2.4-^.2  12.    .240 -5- .2 

Written  Exercise 

182.  Perform  the  operations  indicated.     Check 
the  results. 

1.  17x18.5=?  2.  6.4x7.5=? 

3.  175x1.5=?  4.  12.5  X. 25=? 

5.  17.28 -^  144  6.  95.2 -^  3.4 
7.  28.7  H- 109  8.  67.67-^67 

9.  28.71-9.9     10.    151.3^39     ii.   144  h- 7 

12.  194^9  13.    226 -^  5  i4.    742-^11 

15.  7.23^.4        16.    17.69^7       i7.   45.6^.13 

18.  18.78 -^  .17  19.    How  much  is  i  of  123  ? 

20.  How  much  is  |^  of  560  ? 

21.  How  much  is  |-  of  1780  ? 

22.  Find  1  of  75  23.   Of  39.9 
24.  Of  947                             25.   Of  9003 

26.  How  much  is  81.7  less  -^^  ^^  ^^^  ^ 

27.  From  ^  of  964  take  J  of  435. 

28.  The   quotient   is   9.36,   the   divisor   is    7.3. 
Find  the  dividend. 


136  INTERMEDIATE  BOOK 

29.  Find  the  divisor  when  the  dividend  is  21.42 
and  the  quotient  6.3. 

30.  Find  the  quotient  to  3  decimal  places,  when 
the  dividend  is  .074  and  the  divisor  is  .3. 

Written  Problems 

183.  1.  If  a  man  saves  $  32  a  month,  how  long 
will  it  take  him  to  save  $432? 

2.  If  a  car  conductor  earns  $  2.25  a  day,  how 
long  will  it  take  him  to  earn  $776.25? 

3.  If  9.75  tons  of  coal  cost  $  47.26,  what  is  the 
price  of  1  ton? 

4.  What  is  the  cost  of  12  bales  of  cotton  at 
$.12  a  pound,  if  each  bale  weighs  410.8  pounds? 

5.  Two  motor  cars  start  from  the  same  place 
and  travel  in  opposite  directions,  one  at  15.3  miles 
an  hour,  the  other  at  18.4  miles  an  hour.  How  far 
apart  are  they  at  the  end  of  6.3  hours? 

6.  The  daily  wages  of  each  employee  in  a  factory 
were  increased  $  .18.  The  daily  total  amount  paid 
in  wages  was  thereby  increased  $  84.06.  Find  the 
number  of  employees. 

7.  A  torpedo  boat  has  a  speed  of  38.4  knots  an 
hour.  What  is  its  speed  in  miles,  if  1  knot  is  1.15 
miles  ? 

8.  If  9.8  inches  of  snow  when  melted  make  1 
inch  of  water,  how  much  snow  is  necessary  to 
make  .55  inch  of  water? 


REVIEW 


137 


9.  If  a  merchant  buys  125  suits  of  clothes  at 
$  13.25  each  and  sells  them  at  $  22.50  each,  what 
is  his  profit  ? 

10.    Find  the  product  of  the  sum  and  the  differ- 
ence of  43.25  and  13.76. 

184. 


FRACTIONS 

FREQUENTLY   USED 

IN 

BUSINESS 

10^=^$^ 

25^  =  $i 

121^  =  $i 

50^  =  $| 

75^  =  $!' 

i6f^=n 

20^  =  $^ 

40^  =  $f 

331^  =  $! 

Oral  Exercise 
185.   Find  the  cost.     Use  fractions. 


Quantity 

Kate 

Quantity 

Eatb 

Quantity 

Bate 

1.  32  1b. 

12iJ^ 

6.  40  oz. 

20^ 

11.   36doz. 

^H^ 

2.   18  1b. 

161^ 

7.   80  bu. 

25^ 

12.   96  yd. 

121  f^ 

3.   16  1b. 

75  f 

8.   32  bu. 

11.25 

13.   60bbl. 

75  j^ 

4.  24  1b. 

12i^ 

9.  24  ft. 

12i^ 

14.   46  yd. 

$1.50 

5.   15  yd. 

66|)* 

10.   66  yd. 

^1.66f 

15.   32  bu. 

11.12^ 

Written  Problems 
186.   1.    How  long  will  it  take  a  person  to  earn 

$63.25,  if  he  earns  $2.75  a  day? 

2.    A  train  runs  at  the  rate  of  36.5  mi.  per  hour. 
How  long  will  it  take  to  run  277.4  mi.? 


138  INTERMEDIATE  BOOK 

3.  The  area  of  a  floor  is  396.8  sq.  ft. ;  its  length 
is  25.6  ft.     Find  its  width. 

4.  How  long  will  it  take  a  man  to  walk  8035 
mi.,  if  he  walks  3.75  per  hour  ? 

5.  A  factory  employs  305  men  who  work  8  hr. 
per  day.  If  the  daily  payroll  is  $  512.40,  what  is 
the  average  wage  paid  per  hour  ? 

6.  A  farmer  paid  three  men  $  72  to  shock  his 
corn,  wages  being  $  1.50  a  day.  How  many  days 
did  each  man  work? 

7.  A  steel  rail,  30  ft.  long,  weighs  72  lb.  per 
yard.  How  many  men  are  needed  to  carry  it,  if 
each  man  carries  120  lb.? 

8.  A  city  lot  containing  950  sq.  ft.,  and  190  ft. 
deep,  sells  for  $  1560.  What  was  the  price  per 
foot  of  frontage? 

9.  How  many  states  the  size  of  Delaware,  2050 
sq.  mi.,  could  be  made  from  Texas,  265,780  sq.  mi.? 

10.  A  man  takes  6  acres  of  city  land,  at  $560 
per  acre,  in  exchange  for  55  acres  of  farm  land. 
What  is  the  value  of  the  farm  land  per  acre  ? 

DrUl  Table 
187.    Multiply: 
1-   fxlf  2.   if  x^ 

5.   21x3  6.   31x5 


REVIEW 

7. 

5fx7 

8. 

5fx9 

9. 

3fxl2i 

10. 

4f  X  161 

11. 

2fx6i 

12. 

5|x2f 

13. 

32.5x7 

14. 

45.62  X  29 

15. 

4.55  X  789 

16. 

14.15x875 

17. 

16.5  X. 081 

18. 

3.7  X. 079 

19. 

.087  X. 097 

20. 

.095  X  .008 

21. 

6.663  X  .63 

22. 

2.34  X. 96 

23. 

.83ix.9i 

24. 

1.5  X  .331 

Divide : 

25. 

l-i 

26. 

i-i 

27. 

ff-A 

28. 

f-l 

29. 

A-t 

30. 

10 -2f 

31. 

20^31 

32. 

36-^A 

33. 

35^31 

34. 

3f^9 

35. 

4f-^20 

36. 

61^12 

37. 

121^121 

38. 

91-61 

39. 

4t-5i 

40. 

35.5^.75 

41. 

6.3-^.25 

42. 

.331^.121 

43. 

.661^.161 

44. 

.75^.871 

45. 

.625^.25 

46. 

42.15  H- .625 

47. 

.625^.871 

48. 

.897^.789 

49. 

3.75^.0375 

50. 

.0062^.0012 

139 


DENOMINATE   NUMBERS 
Study  Exercise 

188.  All  numbers  are  either  abstract  or  concrete. 
A  concrete  number   is  one  that  refers  to  par- 
ticular objects,  as,  25  sheep,  46  feet,  72  bushels. 

An  abstract  number  is  one  that  does  not  refer  to 
particular  objects,  as,  7,  8,  13,  16. 

A  denominate  number  is  a  particular  kind  of 
concrete  number  expressing  measure  of  size  or 
weight,  as,  7  feet,  4  pounds. 

Thus,  25  houses  is  a  number  that  is  concrete  but 
not  denominate. 

24  days  is  a  number  that  is  both  concrete  and 
denominate. 

A  denominate  number  of  one  denomination  is 
called  a  simple  denominate  number.  If  it  has  two 
or  more  denominations  it  is  called  a  compound  de- 
nominate number.  2  ft.  is  a  simple  denominate 
number.  2  ft.  4  in.  is  a  compound  denominate 
number. 

Oral  Exercise 

189.  1.    Name  six  abstract  numbers. 

2.  Name  six  concrete  numbers. 

3.  Name  a  concrete  number  that  is  not  de- 
nominate.    Name  one  that  is  denominate. 

140 


DENOMINATE  NUMBERS  141 

Tables 


190.    Memorize 


LINEAR  MEASURE 

12  inches  (in.  or  ")  =  1  foot  (ft.  or  ') 
3  feet  =  1  yard  (yd.) 

16.5  feet  =  1  rod  (rd.) 

320  rods  =  1  mile  (mi.) 

1760  yards  =  1  mile 

TIME 
60  minutes  (min.)  =  1  hour  (hr.) 

24  hours  =  1  day  (da.) 

7  days  =  1  week  (wk.) 

365  days  or  12  months  (mo.)  =  1  year 

DRY  MEASURE 
2  pints    =  1  quart  (qt.) 
8  quarts  =  1  peck  (pk.) 
4  pecks    =  1  bushel  (bu.) 
32  quarts  =  1  bushel 

WEIGHT 
16  ounces  (oz.)  =  1  pound  (lb.) 
100  pounds  =  1  hundredweight  (cwt.) 

2000  pounds  =  1  ton  (T.) 


Reduction  of  Denominate  Nximbers 
191.   1.    Reduce  9^  yd.  to  inches. 

Explanation 
Since  1  yd.  =  3  ft. 

91x3  =  28  ft.  =28  ft. 

28  X  12  =  336  in.     And  since  1  ft.  =  12  in. 

28  ft.  =  28  X  12  in. 
=  336  in. 


142  INTERMEDIATE  BOOK 

2.  Reduce  234  in.  to  yards. 

Pkocess  Explanation 

1^2  ^^'  Since  12  in.  =  1  ft. 

12)234  in.  234  in.  =  234  -^  12  ft. 

12  =19|ft. 

114               61  yd.  Since  3  ft.  =  1  yd. 

108         3)191  ft.  191  ft.  =  191  ^3  yd. 

6  =  ^2-  yd. 

3.  How  many  inches  in  17  ft.  ?     In  f  ft.  ?     In 
If  ft.  ? 

4.  Change  to  a  fraction  of  a  foot :  9  in.,  6  in., 
2  in.,  8  in.,  10  in. 

5.  How  many  feet  in  73  yd.  ?     In  4^  yd.  ?     In 
I  yd.? 

6.  Change  to  rods :  121  yd.,  11  yd.,  66  yd. 


Oral  Exercise 
192.   Reduce  to  inches : 

1.  2  ft.,  21  ft.,  2  ft.  3  in.,  3  ft.  2  in. 

2.  2^  ft.,  4^  ft.,  31  ft.,  lOjL  ft- 

3.  3f  ft.,  2|  ft.,  4|  ft.,  J5  ft. 

4.  51  ft.,  If  ft.,  7f  ft.,  6A  ft. 

5.  4A  ft.,  2Yj  ft.,  3^  ft.,  4^5_  ft. 

6.  5,iv  ft.,  6^^  ft.,  J^  ft.,  411  ft. 

7.  Change  to  ounces :  4  lb.,  2  lb.,  10  oz  ,  2^  lb., 
31  lb..  If  lb. 


DENOMINATE  NUMBERS  143 

8.  How  many  hours  in :  2  da.  ?  21  da.  ?  If  da.  ? 
21  da.  ?  f  da.  ? 

9.  Reduce  to  minutes :  1^  hr.,  2^  hr.,  3^  hr., 
J^  hr    ^^  hr 

10.  Reduce  to  seconds:  ^V  i^i^.,  -^  mm.,  -^ 
min.,  ^  min. 

11.  How  many  days  in  21  wk.  ?  in  3f  wk.  ?  in 
31  wk.? 

12.  In  reducing  from  larger  or  higher  units  to 
smaller  or  lower  units,  do  you  multiply  or  divide  ? 

13.  How  many  bushels  or  parts  of  bushels  in  8 
pk.  ?  in  10  pk.  ?  in  12  pk.  ?  in  14  pk.  ? 

14.  Change  to  pecks  or  parts  of  pecks :  8  qt., 
16  qt.,  12  qt.,  20  qt. 

15.  Reduce  to  quarts :  8  pt.,  9  pt.,  10  pt.,  11  pt. 

16.  In  reducing  from  smaller  or  lower  units  to 
larger  or  higher  units,  do  you  multiply  or  divide  ? 

Written  Exercise 

193.  1.  A  grocer  buys  apples  at  $  1.25  a  bushel 
and  sells  them  at  50^  a  peck.  Find  his  profit  on 
one  bushel. 

2.  A  bushel  of  peanuts  costing  $  1.35  is  sold  at 
5^  a  pint.     What  is  the  gain  ? 

3.  A  coal  dealer  sells  coal  by  the  sack  (weighing 
100  lb.)  at  the  rate  of  25^  each.  What  is  his 
profit  per  ton,  if  he  buys  the  coal  at  $  3  a  ton  ? 


144  INTERMEDIATE  BOOK 

4.  A  man  works  8  hr.  daily;  at  this  rate  how 
many  hours  does  he  work  in  3  weeks  (omitting 
Sundays)  ? 

5.  A  man's  business  office  is  420  rd.  from  his 
home.  If  he  walks  to  his  office  and  back  once 
every  day,  how  many  miles  does  he  walk  in  16  days  ? 

6.  If  pears  cost  $  1.35  a  bushel  and  are  sold  at 
60^  a  peck,  what  is  the  profit  on  2  bu.  ? 

7.  A  dealer  sells  peanuts  at  3j^  a  bag.  If  two 
bags  hold  3  pints,  how  much  does  he  get  in  selling 
1  pk.  of  peanuts  ? 

8.  How  much  cheaper  is  it  to  buy  a  pound  of 

candy  at  30^  a  pound  than  at  the  rate  of  10^  for 

4  ounces  ? 

Tables 
194.    Memorize. 


SQUARE  MEASURE 

144  square  inches  (sq.  in.)  =  1  square  foot  (sq.  ft.) 

9  square  feet  (sq.  ft.)       =  1  square  yard  (sq.  yd.) 
640  acres  (A.)  =  1  square  mile  (sq.  m.) 

LIQUID   MEASURE  COUNTING 

2  pints  (pt.)    =  1  quart  (qt.)  12  units   =  1  dozen  (doz.) 

4  quarts  (qt.)  =  1  gallon  (gal.)  1 2  dozen  =  1  gross 


Study  Exercise 

195.  1.  Draw  a  diagram  and  explain  why  it  is 
that,  while  3  ft.  =  1  yd.,  it  takes  9  sq.  ft.  to  make 
1  sq.  yd. 


DENOMINATE  NUMBERS  145 

2.  In  the  same  way,  explain  why  it  takes  144 
sq.  in.  to  make  1  sq.  ft. 

3.  Pace  the  distance  of  a  little  over  200  ft. 
(208  -^  ft.).  Then  imagine  a  square  that  long 
and  wide.  This  square  covers  one  acre.  How 
many  feet  of  fence  are  needed  to  inclose  this 
square  ? 

Oral  Exercise 

196.  1.   How  many  square  inches  in  2  square  feet  ? 

2.  How  many  square  feet  in  13  square  yards  ? 

3.  How  many  acres  in  100  square  miles  ? 

4.  How  many  quarts  in  12  gallons,  liquid 
measure  ? 

5.  How  many  units  in  one  gross  ? 

6.  How  many  square  yards  in  27  square  feet  ? 

7.  How  many  square  miles  in  6400  acres  ? 

8.  How  many  dozen  in  84  units  ? 

Study  Exercise 

197.  Eeduce  435  in.  to  feet  and  inches  (avoiding 
fractions). 

Process 

36  ft.  Explanation.  —  The  answer  is  36 

12)435  in.  ft.  3  in.     Notice  that  the  remainder  3 

36  is  inches. 

75  The    dividend    and    remainder    are 

72  always  the  same  kind  of  measure. 
3  in. 


146  INTERMEDIATE  BOOK 

Written  Exercise 
198.  1.    Reduce  1179  sq.  ft.  to  sq.  yd. 

2.  Reduce  1290  sq.  ft.  to  sq.  yd.  and  sq.  ft. 
(avoiding  fractions). 

3.  If  5280  ft.  make  a  mile,  how  many  square 
feet  make  a  square  mile  ? 

4.  Reduce  37  gallons  to  pints. 

5.  A  small  farm  contains  160  acres.  What 
part  of  a  square  mile  is  this?  How  many  such 
farms  can  there  be  on  a  square  mile  ? 

6.  A  town  lot  is  20  yd.  wide  and  180  ft.  deep. 
How  many  yards  of  fence  will  inclose  it  ?  What 
is  its  area  in  square  yards  ? 

7.  A  farmer  bought  60  acres  of  timber  land  in 
South  Texas  at  $46.75  an  acre.  Then  he  paid 
$  12.25  an  acre  for  clearing  the  land.  How  much 
was  his  total  outlay  ? 

8.  On  39  acres  he  plants  rice  and  the  yield  is 
worth  $45  an  acre;  10  acres  planted  with  corn 
yield  40  bushels  per  acre,  worth  78^  a  bushel; 
1  acre  yields  strawberries  that  sell  for  $  150. 
Find  the  total  value  of  the  crops. 

9.  Multiply  5|-  by  5J.  Then  explain  why  it  is 
that  SOJ  sq.  yd.  make  1  sq.  yd. 

10.  Reduce  20|-  bu.  to  quarts.     To  pecks. 

11.  How  many  quarts  in  7  bu.  3  pk.  and  7  qt.  ? 
The  liquid  quart  is  less   than  the  dry  quart.     4 


DENOMINATE  NUMBERS  147 

liquid   quarts   make    1  gal.,  but   it   takes  8    dry 
quarts  to  make  1  pk. 

12.  If  31.5  gal.  make  a  barrel,  and  2  barrels  a 
hogshead,  how  many  gallons  are  there  in  13| 
hogsheads  ? 

13.  How  many  bushels  in  564  pecks?  In  164 
dry  quarts  ? 

14.  A  merchant  buys  blackberries  at  12^  cents  a 
quart  and  sells  them  at  $.23  a  quart.  What  is  his 
profit  on  68  quarts  ? 

15.  A  milkman  buys  8  gallons  of  milk  at  $.15  a 
gallon  and  sells  it  at  $.07|-  a  quart.  Find  his 
profit. 

16.  How  many  pounds  and  ounces  are  there  in 
450  oz.  ? 

17.  How  many  hundredweight  are  there  in  7 J 
tons  ?     How  many  pounds  ? 

18.  Which  is  more,  45  hundredweight  or  2^  tons  ? 
How  much  more  ? 

19.  What  is  the  difference  in  weight  between  a 
gross  ton  and  the  ordinary  ton  ? 

20.  A  man  sells  7^  tons  of  coal  at  $  3.25  a  ton. 
Find  the  selling  price. 

21.  Change  26  lb.  3  oz.  to  ounces. 

22.  Change  8000  lb.  to  hundredweight,  also  to 
tons. 

23.  How  many  pounds  in  5  T.  IS^  cwt.  ? 


148 


INTERMEDIATE  BOOK 


Written  Problems 

199.    Study  the  daily  army  ration. 

Daily  army  rations  to  a  United  States  soldier  in 
garrison  comprise  the  following  articles,  measured 
in  ounces : 


Fresh  beef 

20 

Prunes                    1.28 

Flour 

18 

Coffee                     1 12 

Baking  powder 

.08 

Sugar                      3.2 

Beans 

2.4 

Evaporated  milk     .5 

Potatoes 

20 

Salt                           .64 

Black  pepper 

.04 

Lard                         .64 

Cinnamon 

.014 

Butter                      .5 

Flavoring  extract  .014 

1.  How  many  soldiers  can  be  rationed  for  one 
day  on  96  oz.  salt? 

Process  Explanation.  — .  64  oz.  salt 

96  -^  .64  =  150    Arts,      supply  one  soldier  for  one  day. 

96   oz.    salt   supply   as    many 
soldiers  for  one  day  as  .64  is  contained  in  96. 

2.  How  many  soldiers  can  be  rationed  for  one 
day  from  each  amount  named  below  ? 


48  oz.  salt 
12  oz.  black  pepper 
10-lb.  keg  of  butter 
1  cwt.  of  sugar 
100  lb.  potatoes 
96  lb.  beans 
180  lb.  flour 


7  oz.  cinnamon 

6  lb.  lard 

3  lb.  flavoring  extract 

70  lb.  coffee 

64  lb.  prunes 

16  lb.  baking  powder 

500  lb.  beef 


DENOMINATE  NUMBERS  149 

3.  How  many  days  can  10  soldiers  be  rationed 
from  each  amount  named  below  ? 

11  lb.  sugar  8.4  oz.  baking  powder 

183|  lb.  flour  252  lb.  8  oz.  beef 

13f  lb.  beans  65|  lb.  potatoes 

77.3  lb.  prunes  76.4  lb.  coffee 

46  lb.  15  oz.  milk  120  lb.  13.6  oz.  salt 

13|-  lb.  black  pepper  23.96  oz.  cinnamon  " 

6.9  lb.  lard  212  lb.  3  oz.  butter 

PRACTICAL  EXERCISES  AND  PROBLEMS 

Written  Problems 

200.  1.  One  year  there  passed  through  the  canals 
at  the  "  Soo  "  about  90  million  bushels  of  wheat 
and  60  million  bushels  of  other  grain.  How  many 
million  bushels  of  grain  were  shipped  through  the 
"  Soo  "  ? 

2.  How  much  more  wheat  is  carried  than  other 
grain  ? 

3.  Duluth  and  Superior  have  together  27  grain 
elevators  with  a  joint  capacity  of  35  million  bushels. 
Buffalo  has  28  elevators  with  a  joint  capacity  of  23 
million  bushels.  How  much  smaller  is  the  average 
capacity  of  a  Buffalo  elevator  ? 

4.  If  it  takes  4|  bu.  of  grain  for  one  barrel  of 
flour,  how  many  million  barrels  of  flour  are  ob- 
tained from  150  million  bushels  of  grain  ?  Does 
the  answer  exceed  31^  million  barrels? 


150  INTERMEDIATE  BOOK 

5.  Besides  the  grain  there  passed  through  the 
"  Soo  "  locks  about  71  million  barrels  of  flour.  Add 
this  to  the  31^  million  barrels. 

6.  If  one  barrel  of  flour  yields  250  one-pound 
loaves  of  bread,  how  many  million  loaves  can  be 
made  from  39  million  barrels  of  flour  ? 

7.  Allowing  each  individual  1  loaf  a  day,  how 
many  days  would  this  supply  New  York  City, 
which  has  a  population  of  3^  million  ? 

8.  How  many  common  years  and  days  is  this  ? 

9.  Allowing  each  individual  1  loaf  a  day,  how 
many  days  would  this  amount  of  bread  supply  the 
90  million  inhabitants  of  the  United  States  ? 

10.  How  many  months  and  days  would  this  be, 
counting  30  days  to  a  month  ? 

11.  16  million  tons  of  coal  were  transported 
in  one  year  on  Lake  steamers.  If  this  coal  were 
sold  in  equal  amounts  to  each  individual  in  a  city  of 
500,000  inhabitants,  how  many  tons  would  each 
person  get  ? 

12.  If  a  vessel  carries  a  cargo  of  10,000  T.  of 
coal,  how  many  vessels  would  be  required  to  carry 
16  million  T.  ? 

13.  If  such  a  cargo  of  coal  can  be  loaded  on  a 
ship  in  12  hours,  how  many  tons  are  loaded  per 
hour  ? 

14.  Find  the  cost  of  transporting  8  million  T.  of 
coal  on  the  Lakes  from  the  East  to  Duluth,  a  dis- 


DENOMINATE  NUMBERS 


151 


tance  of  about  1000  rni.,  at  $.35  a  ton.     What  is 
the  cost  of  transportation  per  mile  ? 

15.  On  an  average,  one  large  freight  vessel  passes 
from  Lake  Huron  through  the  Detroit  River  to 
Lake  Erie  every  12  minutes,  day  and  night,  during 
the  8  months  of  navigation.  How  many  vessels 
pass  in  8  months  (of  30  days  each)  ? 

16.  One  year  there  were  571  steel  ships  carrying 
freight  on  the  Great  Lakes.  What  was  the  average 
tonnage,  if  the  tonnage  of  all  ships  was  2  million  ? 


Written  Problems 

201.   1.    Study  and  compare  the  height  of  tall 
buildings  in  New  York  City. 


Building 

Height  in  Fket 

No.  OF  Stories 

Trinity  Church 

Flatiron 

234 

286 

375.5 

382 

419 

617 

700 

750 

909 

20 

Pulitzer 

Park  Row 

22 
26 

Times 

28 

Sinerer .     . 

42 

Metropolitan    . 

Woolworth 

New  Equitable  (plan) 

46 
51 
62 

2.  How  much  higher  will  the  New  Equitable 
building  be  than  the  Trinity  Church,  Flatiron,  and 
Pulitzer  taken  together  ?  Than  the  Park  Row  and 
Times  combined  ? 


152  INTERMEDIATE  BOOK 

3.  Compute  to  a  tenth  of  a  foot  the  average 
height  of  a  story  in  each  building.  Which  has  the 
highest  stories  ? 

4.  How  many  times  higher  will  the  New  Equi- 
table be  than  Trinity  Church?  Than  the  Times 
building  ? 

5.  The  flagpole  of  the  New  Equitable  will  extend 
150  feet  above  the  top  of  the  building.  How  far 
above  the  street  will  the  flag  float  ? 

6.  The  Eiffel  tower  in  Paris  is  75  feet  higher 
than  the  New  Equitable  will  be.  How  much  higher 
than  the  Eiffel  tower  will  the  flag  on  the  New 
Equitable  be  ? 

7.  The  New  Equitable  will  have  8  passenger 
elevators  running  all  the  way  to  the  top.  What  is 
the  combined  length  of  the  8  elevator  shafts  ? 

8.  If  the  New  Equitable  elevators  travel  600 
feet  a  minute,  how  long  will  it  take  an  elevator  to 
travel,  without  stops,  from  the  ground  floor  to  the 
top? 

9.  The  Metropolitan  is  built  on  ground  75  ft. 
square ;  that  is,  75  ft.  long  and  75  ft.  wide.  The 
Singer  on  ground  65  ft.  square.  By  how  many 
square  feet  does  the  former  ground  exceed  the 
latter? 

10.  The  Metropolitan  Tower  has  a  clock  with  a 
dial  25^  feet  in  diameter.  The  circumference  of  a 
circle  is  about  3.14  times  the  length  of  the  diameter. 


DENOMINATE  NUMBERS 


153 


How  far  is  it  around  this  dial  ?  How  many  feet 
must  the  extremity  of  the  gigantic  minute  hand 
move  every  minute  ? 

Gas  Meter 

202.   A  gas  meter  has  three  dials.     By  reading 
these  dials  we  can  find  the  number  of  cubic  feet  of 


^9^^T^ 


March  4,  1914 


^-^^^ 


^"PT^       \P^f^ 


April  3,  1914 

gas  used.  The  figures  on  the  dial  at  the  right  denote 
hundreds  of  cubic  feet,  the  figures  of  the  middle 
dial  denote  the  thousands  of  cubic  feet;  the  fig- 
ures on  the  dial  at  the  left  denote  ten  thousands  of 
cubic  feet. 

While  the  hand  of  the  right  dial  makes  one  revo- 
lution, the  hand  of  the  middle  dial  moves  through 
one  division:  while  the  hand  of  the  middle  dial 


154 


INTERMEDIATE  BOOK 


makes  one  revolution,  the  hand  of  the  left  dial 
moves  through  one  division. 

The  dials  are  read  from  left  to  right  by  taking  the 
figures  which  the  hands  have  just  passed. 

Thus,  the  meter  in  the  picture  above  gives  the 
figures  3,  6,  1.  This  means  30,000  en,  ft.  plus 
6,000  cu.  ft.  plus  100  cu.  ft.  =  36,100  cu.  ft. 


Notice  that  it  is  necessary  only  to  write  361  and 
annex  two  zeros. 

1.  The  figure  shows  the  meter  in  Mr.  Jackson's 
house  on  March  4,  1914,  and  on  April  3,  1914. 
Read  the  meter  for  each  date. 

2.  How  many  cubic  feet  of  gas  were  consumed 
from  March  4  to  April  3  ? 

What  was  the  cost  of  the  gas  at  $  1  per  1000 
cu.  ft.  ? 


DENOMINATE    NUMBERS 


155 


3.  At  $1  per  1000  cu.  ft.,  what  is  the  cost  of 
4,320  cu.  ft.  ?     Of  800  cu.  ft.  ?     Of  76,800  cu.  ft.  ? 

4.  The  following  is  a  gas  bill  sent  to  Mr.  A.  Hart : 


SCo  Consolidated  Qas  Company  of  New  York,  JBr« 

Branch  Offiice,  133  EAST  15th  STREET,  near  Irving  Place 
TELEPHONE  4901   STUYVESANT 


cA&w-  yo-ik  ^itif 


For  Gas  Supplied  from  j/o/^.  /,\oS&(y:  f,  191(5"  Arrears 191 

Present  State  of  Meter    76,8  00  


Previous  State  of  Meter    7^,^00  

/ ,  ^  00  cubic  feet  of  Gas  at  80c  per  M 


This  charge  is  made  in  con- 
formity with  the  opinion  and 
decree  of  the  Supreme  Court 
of  the  United  States  rendered 
in  the  suit  brought  on  May  i, 
1906,  by  the  Consolidated  Gas 
Company  of  New  York  in  the 
United  States  Circuit  Court. 

Received  payment for  the  Company. 


62 


Make  a  bill  for  Example  i  similar  to  the  one 
shown  here. 

5.  If  an  ordinary  gas  burner  consumes  6  cu.  ft. 
of  gas  per  hour  and  a  Welsbach  burner  consumes 
4  cu.  ft.  per  hour,  how  many  cubic  feet  will  both 
consume  in  Vl\  hr.  ? 

6.  If  gas  costs  $  1  per  1000  cu.  ft.,  how  much 
is  saved  in  a  month  of  30  da.  by  using  the  Welsbach 
burner  ? 


156 


INTERMEDIATE  BOOK 


7.  At  various  times  read  the  gas  meter  in  your 
home  or  the  home  of  a  friend,  and  make  out  bills 
for  gas  consumed,  using  the  rate  actually  charged. 


203. 


Time  Tables 


Condensed  Time,  Chicago  to  Omaha 


Read  Down 


Read  Up 


Limited 
Daily 

Express 
Daily 

Mi. 

9:16  a.m. 

10:32  P.M. 

0 

10:21  A.M. 

11:44  P.M. 

40 

12:10  P.M. 

1:87  A.M. 

114 

2:00  P.M. 

2:26  a.m. 

183 

8:45  P.M. 

8:40  A.M. 

358 

8:60  P.M. 

8:45  A.M. 

358 

11:06  P.M. 

1:10  P.M. 

603 

Stations 
Eock  Island  Lines 


Limited 
Daily 


Express 
Daily 


Lv Chicago.  ..Ar. 

Joliet 

Bureau 

Davenport . . . 

Ar.  Des  Moines  Lv. 
Lv.  "  "  Ar. 
Ar.  .  ..Omaha.  ..Lv. 


4:59  P.M. 

z 
2:10  P.M. 
12:25  P.M. 
7:36  A.M. 
7:20  A.M. 
3:00  A.M. 


7:25  A.M. 
6:20  a.m. 
4:25  A.M. 
2:35  A.M. 
9:42  P.M. 
9:30  P.M. 
4:40  P.M. 


z  Trains  stop  to  let  off  passengers  from  Colorado  and  Points  west. 


1.  What  are  the  terminal  points  given  in  this 
table  ? 

2.  What  other  cities  are  given  ? 

3.  How   many   trains  are  given  in  this  table? 
Which  run  west  ?     Which  run  eastward  ? 

4.  Name   the   time   the  former  leave  Chicago; 
also  the  time  the  latter  leave  Omaha. 

5.  How  long  a  stop  do  the  trains  make  in  Des 
Moines? 

6.  How  far  is  it  from  Des  Moines  to  Omaha? 
From  Joliet  to  Davenport  ? 


DENOMINATE    NUMBERS  157 

7.  In  what  time  does  the  westbound  express 
run  from  Bureau  to  Davenport  ?  From  Des  Moines 
to  Omaha? 

8.  In  what  time  does  the  morning  train  run 
from  Omaha  to  Davenport  ? 

9.  What  is  the  fare  from  Chicago  to  Des  Moines 
at  2^  a  mile?     At  3^  a  mile? 

10.  Can  a  passenger  from  Colorado,  passing 
through  Omaha  in  the  morning,  get  off  at  Joliet  ? 

11.  In  what  time  does  each  of  the  four  trains 
travel  between  Chicago  and  Des  Moines  ?  Between 
Des  Moines  and  Omaha  ? 

12 .  What  is  the  distance  of  each  city  from  Chicago  ? 

Areas 
204.   1.   Review  square  measure.  Art.  194. 

2.  A  plane  figure  is  a  part  of  a  plane  bounded 
by  straight  or  curved  lines. 

3.  Construct  with  ruler  a  plane  figure  bounded 
by  four  straight  lines.  How  many  sides  has  the 
figure  ?     How  many  corners  or  angles  has  it  ? 

4.  A  plane  figure  bounded  by  four  straight  lines 
is  called  a  quadrilateral. 

5.  Construct  a  quadrilateral  that  has  square 
corners,  or  right  angles.    What  is  this  figure  called  ? 

6.  A  rectangle  is  a  quadrilateral  whose  angles 
are  right  angles. 


158 


INTERMEDIATE  BOOK 


7.  In  the  figure  how  many  squares  in  each  row? 
How  many  rows  are  there?  If  each  square  is 
one  square  inch,  how  many  square  inches  in  the 
area  of  the  figure  ? 

8.  How  is  the  area  of 
any  rectangle  found  ? 

9.  The  area  of  a  rec- 
tangle is  the  base  times  the 
altitude. 


10.    A  triangle  is  a  plane 
figure  bounded  by  3  straight  lines. 

11.  The  line  on  which  a  rectangle  or  a  triangle 
stands  is  called  its  base. 

12.  How  does  the  shaded  triangle  A  compare  in 
area  with  the  rectangle  A  ? 

13.  How  does  the  shaded  part  in  B  (triangle  B) 
compare  in  area  with  the  rectangle  B  ? 

14.  In  A  the  rectangle  and  the  triangle  have  the 
same  base  and  the  same  height.  Is  this  true  of  B  ? 
A  triangle  is  exactly  half  the  rectangle  of  the  same 
base  and  height. 

15.  The  area  of  the  triangle  is  the  base  times 
the  altitude,  divided  by  2. 

16.  If  rectangle  A  is  10  sq.  in.,  what  is  the  area 
of  triangle  A  ? 

17.  If  rectangle  B  measures  16  sq.  in.,  what  is 
the  area  of  triangle  B  ? 


DENOMINATE  NUMBERS 


159 


18.  If  rectangle  B  is  6  in.  long  and  4  in. 
high,  what  is  its  area?  What  is  the  area  of 
triangle  B? 


Rectangle  A 

Triangle  A  (the  shaded 

part)  . 


Rectangle  B 

Triangle  B  (the  shaded 

part)  . 


19.    The  perimeter  of  a  triangle  or  rectangle  is  the 
sum  of  the  lengths  of  its  sides. 

Written  Exercise 
205.    Find  the  areas  : 


Rectangles 


Base 

Height 

Base 

Height 

1.  36  ft. 

105  ft. 

11. 

175  ft. 

348^  ft. 

2.  79  ft. 

437  ft. 

12. 

175  ft. 

myd. 

3.  63  ft. 

84  in. 

13. 

96  ft. 

2^  rd. 

4.  48  in. 

4  ft. 

14. 

180  rd. 

29f  rd. 

5.  96  in. 

5  yd. 

15. 

274f  rd. 

48f  yd. 

6.  100  in. 

6rd. 

16. 

29|  yd. 

17i  ft. 

7.  50  yd. 

10.5  ft. 

17. 

75.79  rd. 

18.80  rd. 

8.  127  yd. 

37.75  ft. 

18. 

96.37  ft. 

29.98  ft. 

9.  40  rd. 

19.66  yd. 

19. 

48.24  yd. 

3.48  rd. 

10.  80  rd. 

28.8  rd. 

20. 

.75  in. 

.8  in. 

160 


INTERMEDIATE  BOOK 


Triangles 


Babe 

Height 

Base 

Height 

1.    4|ft. 

5A  ft. 

11. 

1  ft.  4  in.    • 

3  ft.  7  in. 

2.    7§in. 

6|in. 

12. 

5  ft.  8  in. 

4  ft.  6  in. 

3.   8iyd. 

7fft. 

13. 

25  ft.  11  in. 

16  ft.  9  in. 

4.   25.5  rd. 

12.8  rd. 

14. 

12  ft.  10  in. 

20  ft.  5  in. 

5.   36.87  rd. 

14.24  rd. 

15. 

3  yd.  2  ft. 

4  yd.  1  ft. 

6.   5fyd. 

6.8  yd. 

16. 

5  yd.  1  ft. 

1  yd.  2  ft. 

7.   28.48  in. 

2|yd. 

17. 

8  rd.  2  yd. 

2  rd.  2  yd. 

8.    18.5  ft. 

18.5  ft. 

18. 

3  rd.  2  ft. 

4  rd.  6  ft. 

9.   12|in. 

12|  in. 

19. 

5  rd.  1  ft. 

4  rd.  1  ft. 

10.    10.5  in. 

20,5  in. 

20. 

10  rd.  10  ft. 

10  rd.  10  ft. 

Written  Problems 

206.  1.  The  pages  of  a  book  are  5^  in.  wide  and 
10  in.  high.  How  many  square  inches  in  the  area 
of  the  page  ? 

2.  If  one  of  these  pages  is  cut  in  two  from 
corner  to  corner,  what  is  the  area  of  each  part  ? 

3.  An  envelope  is  4  in.  by  5 J  in.  How  many 
square  inches  in  its  area  ? 

4.  What  is  the  area  of  a  postage  stamp  ^  in.  by 

5.  Which  covers  the  greater  surface,  a  triangle 
with  a  base  of  8  in.  and  an  altitude  of  7  in.,  or  a 
triangle  with  a  base  of  6  in.  and  an  altitude  of 
9  in.  ? 

6.  The  first  baseman,  second  baseman,  and 
catcher  are  on  the  corners  of  a  triangle.     Call  the 


DENOMINATE  NUMBERS  161 

line  from  the  home  plate  to  first  base  the  base 
of  the  triangle  and  the  line  from  the  first  to  the 
second  base  its  height.  The  base  and  height  are 
each  90  ft.  Find  the  area  of  the  triangle  in  square 
feet.    Also  in  square  yards. 

7.  A  mason  has  1000  tiles,  each  ^  ft.  square 
(that  is,  ^  ft.  long  and  ^  ft.  wide).  How  many 
square  feet  of  floor  can  he  lay  with  them  ? 

8.  A  cement  walk  35 J  ft.  long  and  6  ft.  wide 
costs  10^  a  square  foot.     What  is  its  total  cost? 

9.  A  rug  is  7  yd.  by  6|-  yd.  How  much  larger 
is  this  than  another  rug  6  yd.  by  7  yd.  ? 

10.  How  many  square  yards  of  wall  can  be 
covered  with  a  roll  of  paper  ^  yd.  wide  containing 
85  yd.  ? 

11.  A  public  hall  is  150  ft.  long  and  20  yd.  wide. 
Find  its  floor  space  in  square  feet. 

12.  A  rectangular  garden  is  17^  yd.  long  and 
lOi  yd.  wide.  How  many  yards  of  fencing  would 
it  take  to  inclose  it  ?  How  many  square  yards  of 
ground  in  the  garden  ? 

13.  Which  is  more,  a  piece  of  ground  25|  rd.  by 
10  rd.,  or  one  containing  two  acres  ? 

14.  How  many  acres  of  land  are  there  in  I-  sq.  mi.  ? 

15.  One  flower  bed  is  35  ft.  by  20  ft.,  another  is 
70  ft.  by  10  ft.  Find  their  perimeters.  Find  their 
areas.  Can  two  rectangles  have  equal  areas  but 
different  perimeters  ? 


162  INTERMEDIATE  BOOK 

16.  A  teacher  orders  a  slate  blackboard  with  a 
wooden  molding  around  it.  If  the  blackboard  is 
to  be  2 1  yd.  long  and  1|  yd.  wide,  how  many  square 
yards  of  slate  must  be  ordered  ?  How  many  yards 
of  molding  ? 

17.  In  making  boxes,  pieces  are  cut  from  sheets 
of  pulp  board  so  as  to  waste  as  little  as  possible. 
How  many  pieces,  each  2''  x  2'',  can  be  cut  from  a 
sheet  14''  by  W  ?     Can  waste  be  avoided  ? 

18.  How  many  pieces,  each  3"  x  4'',  can  be  cut 
from  a  sheet  15''  x  16"  ?     Can  waste  be  avoided  ? 

19.  How  many  pieces,  each  4''  x  5",  can  be  cut 
from  a  sheet  16" x  18"?     Can  waste  be  avoided? 

20.  Make  similar  problems  of  your  own  in  which 
there  is  waste.     In  which  there  is  no  waste. 

21.  From  one  sheet,  make  a  box,  without  cover, 
of  the  dimensions  5"  x  3"  x  2".  How  large  a  sheet 
is  needed? 

22.  Draw  a  similar  figure  showing  the  sheet 
needed  in  making  a  box  7"  x  4"  x  3".  How  much 
is  the  waste  ? 

23.  How  much  is  the  waste  in  making  from  one 
square  sheet  a  box  4"  x  4"  x  4"  ?  How  large  a  sheet 
is  needed  ? 

24.  How  much  is  the  waste  in  making  a  box 
5"  X  3"  X  2"  from  a  sheet  9"  x  8"  ? 

25.  How  many  covers  the  size  of  this  book  cover 
can  be  made  from  a  piece  of  cloth  1  yd.  square  ? 


DENOMINATE  NUMBERS 
Angles 


163 


Bight  Angle 


Acute  Angle 


Obtuse  Angle 

207.  1.  What'  kind  of  angle  do  the  hands  of  a 
clock  make  at  9  o'clock  ?     At  3  o'clock  ? 

2.  What  kind  of  angle  do  the  hands  of  a  clock 
make  at  10  o'clock  ?     At  11  o'clock? 

3.  When  do  the  hands  form  the  larger  angle,  at 
11  o'clock  or  at  2  o'clock  ? 

4.  What  kind  of  an  angle  do  the  hands  of  a 
clock  form  at  4  o'clock  ?     At  5  o'clock  ? 

5.  Is  the  angle  formed  by  the  hands  larger  at 
8  o'clock  than  at  7  o'clock  ?  At  9  o'clock  than  at 
8  o'clock? 

6.  A  right  angle  has  been 
divided  into  90  equal  parts, 
called  degrees.  Surveyors 
and  draftsmen  usually  give 
the  size  of  angles  by  telling 
the  number  of  degrees  which 
they  contain. 


90  degrees  (90°)  =  1  right  angle 


How  many  degrees  are  there  in  2  right  angles  ? 
In  3  ?     In  1  of  a  right  angle  ?     In  J  ?     In  |  ? 


164 


INTERMEDIATE  BOOK 


Drawing  and  Construction  Exercise 

208.  1.  Measure  the  sides  of  this  triangle  to  find 
its  perimeter. 

2.  Measure  the 
height  of  this  tri- 
angle. Find  its  area 
in  square  inches. 

3.  Find  the  area 
of  a  triangle  which 

is  twice  as  high  and  has  a  base  twice  as  long  as 
that  of  the  triangle  shown  in  the  figure. 

4.  Construct  5  triangles.  Measure  the  base  and 
the  altitude  to  find  the  perimeter  and  the  area  of 
each. 

5.  Construct  a  triangle  with  one  angle  a  right 
angle. 

6.  Draw  a  large  triangle  similar  to  the  triangle  in 
Example  i  of  this  exercise. 

Cut  off  the  3  angles  of 
the  triangle  and  set  them 
together  on  one  side  of  a 
straight  line  as  illustrated. 
Then  draw  a  line  as  indicated. 

7.  To  how  many  right  angles  are  the  three 
angles  of  a  triangle  equal  ? 

8.  If  a  right  angle  is  equal  to  90°,  how  many 
degrees  in  all  the  angles  of  a  triangle  ? 


DENOMINATE   NUMBERS  165 

Written  Exercise 

209.  1.  If  the  three  angles  of  a  triangle  are 
equal,  what  part  of  a  right  angle  is  each  ? 

2.  If  two  angles  of  a  triangle  are  each  just  | 
of  a  right  angle,  how  big  is  the  third  ? 

3.  If  one  angle  is  f  of  a  right  angle,  and  an- 
other angle  is  f  of  a  right  angle,  how  much  is  the 
third  angle  ? 

4.  If  two  angles  are  each  f  of  a  right  angle,  how 
large  is  the  third  angle  ? 

5.  If  one  angle  of  a  triangle  is  ^  of  a  right 
angle  and  another  is  |  of  a  right  angle,  what  is 
the  third  angle  ? 

6.  Find  in  the  walls  and  ceiling  of  your  room 
two  lines  forming  a  right  angle. 

7.  Express  in  degrees  the  sum  of  the  angles  of 
a  triangle. 

8.  Two  of  the  angles  of  a  triangle  are  65°  and 
73°.     What  is  the  third  angle  ? 

9.  How  many  right  angles  will  exactly  fill  the 
space  about  a  point  in  a  plane  ? 

10.  A  wheel  has  8  spokes.  What  is  the  angle 
between  two  neighboring  spokes  ? 

11.  Through  how  many  degrees  does  the  minute 
hand  turn  in  an  hour  ?  In  half  an  hour  ?  In  15 
minutes  ?     In  5  minutes  ? 


166  INTERMEDIATE  BOOK 

12.  What  angle  do  the  hour  and  minute  hands 
form  at  1  o'clock  ?     At  2  o'clock  ?     At  5  o'clock  ? 

13.  How  many  degrees  in  each  angle  of  an  equi- 
angular triangle  ? 

14.  How   many  degrees   are   there  in  the  four 
angles  of  a  rectangle  taken  together  ? 

Time 
Exercises  and  Problems 

210.   1.    Compute  the  number  of  seconds  in  one 
day. 

2.  Reduce  90,630  seconds  to  days,  hours,  min- 
utes, and  seconds  (avoiding  fractions). 

3.  Find  the  number  of  seconds  in  ^  of  an  hour. 

4.  Reduce  400  seconds  to  a  fraction  of  an  hour. 

5.  Change  114  hours  to  days. 

6.  How  many  weeks  in    192   days  ?     In   200 
days? 

7.  Which  months  have  31  days  ?     Which  30  ? 
How  many  has  February  ? 

8.  A  clock  ticks  138  times  every  minute.    How 
many  times  in  10  seconds  ?     In  one  hour  ? 

9.  A   man   in  walking   takes  3  steps  every  2 
seconds.     How  many  steps  does  he  take  in  an  hour  ? 

10.   If  he  takes  90  steps  per  minute,  how  many 
does  he  take  per  hour  ? 


DENOMINATE  NUMBERS  167 

11.  If  he  takes  5,400  steps  per  hour,  and  each 
step  measures  3  ft.,  how  many  feet  does  he  travel 
per  hour  ? 

12.  A  man  walks  at  the  rate  of  4  mi.  an  hour.  At 
this  rate,  how  many  rods  will  he  walk  in  20  min.? 

13.  In  a  10-acre  nursery  of  white  ash  trees  there 
were  63  rows  of  trees,  630  trees  in  each  row.  In 
9  weeks  gophers  killed  ^  of  the  trees  by  gnawing 
their  roots.  How  many  trees  were  destroyed  in  9 
weeks  ?     In  1  week  ?     In  1  day  ? 

14.  A  gopher  is  known  to  have  dug  an  under- 
ground burrow  480  ft.  long  in  2  days,  throwing 
up  hillocks  of  loose  earth  at  intervals  of  about  4  ft. 
How  many  hillocks  were  thrown  up  at  this  rate 
in  2  days? 

The  Difference  in  Time  between  Two  Dates 

211.  1.  Find  the  exact  number  of  days  from 
June  16  to  Aug.  24. 

In  June  there  are  14  days  remaining ;  in  July 
there  are  31  days ;  in  August  there  are  24  days  to 
Aug.  24.     Add  14,  31,  24,  to  obtain  the  answer. 

2.  Find  the  number  of  months  and  days  from 
March  4  to  July  10. 

Find  the  whole  number  of  months  and  then  the 
number  of  days  remaining.  From  March  4  to  July 
4  are  4  months.  From  July  4  to  July  10  are  6 
days.     The  answer  is  4  months  and  6  days. 


168  INTERMEDIATE  BOOK 

3.  How  many  days  are  there  from  July  7  to 
July  31  ?  From  Feb.  3  to  Feb.  27  ?  From  March 
16  to  April  25  ? 

4.  Find  the  exact  number  of  days  from  May  3 
to  July  22. 

5.  How  many  months  are  there  from  Jan.  5  to 
June  5  ? 

6.  How  many  even  months  and  how  many 
days  over  from  Feb.  12  to  Sept.  25  ? 

7.  School  opens  Sept.  12  and  closes  June  5. 
How  many  even  months  and  how  many  days  over 
are  there  between  these  dates  ? 

8.  How  many  years,  months,  and  days  between 
Sept.  15,  1875  and  Nov.  24,  1910  ? 

From  Sept.  15,  1876,  to  Sept.  15,  1910,  are  35 
years ;  from  Sept.  15  to  Nov.  15  are  2  months ; 
from  Nov.  15  to  Nov.  24  are  9  days. 

Answer:    35  years,  2  months,  9  days. 

9.  What  was  Benjamin  Franklin's  age  at  the 
time  of  his  death,  born  Jan.  17,  1706,  and  died 
April  17,  1790  ? 

10.  What  was  George  Washington's  age  at  the 
time  of  his  death,  born  Feb.  22,  1732,  and  died 
Dec.  14,  1799  ? 

11.  What  was  Henry  W.  Longfellow's  age  at 
the  time  of  his  death,  born  Feb.  27,  1807,  and 
died  March  24,  1882  ? 


DENOMINATE  NUMBERS  169 

12.  What  was  Abraham  Lincoln's  age  at  the 
time  of  his  death,  born  Feb.  12,  1809,  and  died 
April  15,  1865  ? 

13.  What  was  James  R.  Lowell's  age  at  the 
time  of  his  death,  born  Feb.  22,  1819,  and  died 
Aug.  12,  1891? 

14.  How  many  years  elapsed  between  the  birth 
of  Washington  and  of  Lowell  ? 

15.  How  long  did  Washington  live  after  the 
death  of  Franklin  ? 

16.  How  old  was  Lowell  when  Lincoln  died  ? 

17.  How  old  was  Longfellow  when  Lowell  was 
bom? 

Review  Exercise 

212.  1.  How  many  dimes  make  $  1  ?  Then 
what  part  of  $  1  is  a  dime  ?  What  part  are 
2  dimes?   3  dimes? 

2.  How  many  cents  make  $  1  ?     Then  what  part 
of  $  1  is  a  cent  ?     What  part  are  3  cents  ?  7  cents  ? 

3.  In  $  2.35  there  are  how  many  whole  dollars  ? 
How  many  dimes  ?     How  many  cents  besides  ? 

4.  In  $  4:A4:  what  does  each  digit  stand  for  ? 

5.  What  part  of  a  dollar  is   $0.10?    S0.60? 
$0.70? 

6.  What  part  of  a  dollar  is   $0.05?    $0.09? 
$0.06? 

7.  What  part  of  a  dollar  is  5^  ?   15^  ?   65^  ? 


170  INTERMEDIATE  BOOK 

8.  35^  =  ^,55^'  =  ^,  $0.45  =  ^. 

9.  What  does  each  digit  stand  for  in  $  15.678  ? 
10.    How  does  the  value  of  each  digit  in  $  6.666 

compare  with  the  digit  to  its  right  ?     Which  digit 
has  the  least  value  ?     Which  the  most  ? 

Oral  Exercise 

213.  Tell  how  many  dollars,  cents,  and  mills 
there  are  in : 

1.  $4,765  2.  $10,075  3.  $0,457 

4.  $0,043  5.  $111,111  6  $10 

7.  $.01  8.  $.001  9.  $10.01 

10.  $100.01  11.  $1000.101  12.  $1000.01 

13.  $1001.001  14.  $1,001  15.  $8,663 

Making  Change 

214.  If  you  owe  85^  and  pay  the  debt  with  a 
dollar,  the  storekeeper  gives  you  5  cents  and 
10  cents,  saying  85  and  5  is  90  and  10  is  a  dollar. 

Make  change 

1.  For  $1,  when  some  one  pays  70^. 

2.  For  $  1,  when  some  one  pays  65^. 

3.  For  50^5  when  some  one  pays  35^. 

4.  For  $5,  when  some  one  pays  $2.75. 

Make  change  for  $  1,  $  2,  and  $  5  with  each  of 
the  following  numbers : 


DENOMINATE  NUMBERS  171 


5. 

75f! 

55^ 

45^ 

35^ 

85^ 

45^ 

65^ 

6. 

77^ 

67^ 

15^ 

31^ 

47^ 

66^ 

18^ 

7. 

sy 

62^ 

82  «* 

78^ 

23^ 

21^ 

56^ 

8. 

77^ 

36<^ 

54^ 

52  >^ 

48^ 

34^ 

71^ 

Oral  Exercise 
215.   1.   At  25^  a  yard,  how  many  yards  can  be 
bought  for  $  1  ?     For  $  4  ?     For  $  17  ? 

2.  At  33^^  a  bushel,  how  many  bushels  can  be 
purchased  for  $  2  ?     For  $  10  ?     For  $  15^? 

3.  How  many  yards  of  calico  at  20^  a  yard  can 
be  bought  for  $  920  ? 

4.  $  10  will  buy  how  many  pounds  at  12^^  a 
pound  ? 

5.  $  30  will  buy  b  ow  many  dozen  at  3  3|^^  a  dozen? 

6.  How  many  yards  of  silk  costing  $  1.121  per 
yard  can  be  bought  for  $  243  ? 

7.  How  many  articles  at  $  1.25  each  can   be 
bought  for  $  75  ? 

8.  How  many  articles  costing  33^^  each  can  be 
bought  for  $  20  ?     $  33  ?     $  lOf? 

9.  How  many  12 1^  articles  can  be  bought  for 
$2?     $7?     $15?     $7^? 

10.  How  many  25^  articles  can  be  had  for  $  75? 
$10?     $10.75? 

11.  How  many  66f  ^  articles  can  be  purchased 
for  $10?     $14?     $76? 


THE  ANALYSIS  AND  SOLUTION  OF  PROBLEMS 

216.   1.   If  2  lamp  chimneys  cost  12)^,  what  will 
3  cost  ? 

Analysis 

If  2  chimneys  cost  12^, 

1  chimney  will  cost  J  of  12^,  or  6^. 

3  chimneys  will  cost  3x6^,  or  18^. 

2.  What  is  the  cost  of  5  drinking  glasses,  if  2  of 
them  cost  22^? 

3.  If  3  cakes  of  soap  cost  15^,  what  is  the  cost 
of  2  cakes  ? 

4.  If  2  sugar  bowls  are  sold  for  38^,  what  are 
3  sold  for? 

5.  If  3  coffee  pots  cost  $1.20,  what  will  5  of 
them  cost  ? 

6.  What  is  the  cost  of  2  water  bottles,  if  5  of 
them  cost  $1.25? 

7.  What  do  we  pay  for  7  boxes  of  matches,  if 
2  boxes  sell  for  4^? 

8.  What  is  the  price  of  9  brooms,  if  2  brooms 
cost  30^? 

172 


SOLUTION  OF  PROBLEMS  173 

9.    Trout  is  advertised  at  30^  for  2  lb.     Find 
the  cost  of  5  lb.     Of  10  lb.     Of  11  lb. 

10.   If  5  lb.  of  salmon  cost  $  1,  what  will  9  lb. 
cost? 

Written  Problems 
217.   Analyze  and  solve: 

1.  If  21  gallons  of  gasoline  cost  $  3.54,  what  will 
49  gallons  cost? 

Solution 

3  54 

1  gallon  costs  -j—  dollars, 
zi 

49  gallons  cost  ^'      dollars. 

z  J. 

Cancel  factors  common  to  both  terms,  thus: 
1.18       7 

7 

The  process  is  shorter  if  the  indicated  division  is  sim- 
plified but  not  performed.     Thus,  -^  is  ♦     Then 

3.54  x49     354  X  49      ^         -,  .  ..  ., 

— =  — — .     By  so  doinff  we  oiten  escape  the 

21  2100  ^  ^  ^ 

necessity  of  dividing.     In  any  case,  it  is  better  not  to 

carry  out  the  operations  until  the  last  step. 

2.  What  is  the  cost  of  35  lb.  of  catfish  at  %  2.67 
for  15  lb.  ? 


174  INTERMEDIATE  BOOK 

3.  If  2  gallons  of  benzine  sell  for  25^,  what  is 
the  cost  of  25  gallons? 

4.  If  20  A.  of  land  sell  at  $  310,  what  will  59  A. 
sell  at? 

5.  If    2   acres    of   strawberries    yield    a    crop 
worth  $  259.65,  what  will  121  acres  yield  ? 

6.  At  $  16.50  per  half  dozen  pairs  of  gloves, 
what  will  21  dozen  pairs  cost  ? 

7.  John's  salary  is  $  700  a  year.     What  is  it  for 
7  months? 

8.  If  f  of  an  acre    of   garden  land   sells   for 
$  375,  what  will  i  of  an  acre  sell  for  ?     1  acre  ? 

9.  At  $  5  a  ton  of  2000  lb.,  what  will  3000  lb. 
of  coal  cost?     3500  lb.? 

10.  Mutton  is  quoted  at  $  4.60  a  hundred  pounds. 
How  many  pounds  can  be  purchased  for  $  230  ? 

11.  At  $  5.75  a  hundred  pounds,  find  the  cost  of 
275  lb.  of  lamb. 

12.  Calves  sell   at   $5.10  per  hundred  pounds. 
How  much  will  calves  weighing  2700  lb.  bring? 

13.  Find  the  price  of  cows  weighing  3200  lb. 
at  $  3.25  a  hundred  pounds. 

14.  At  $  30  a  hundred  pounds,  find  the  cost  of 
1875  lb.  of  creamery  butter. 

15.  At   $  9.75   a   hundred   pounds,   7^  tons   of 
timothy  hay  cost  $ . 


SOLUTION  OF  PROBLEMS  175 

16.  If  3  men  can  do  a  piece  of  work  in  6  days, 
how  long  would  it  take  1  man  to  do  this  work  ? 

17.  How  long  will  it  take  10  masons  to  build  a 
certain  foundation  for  a  house,  if  3  masons  can  do 
it  in  20  days  ? 

18.  If  50  ft.  of  garden  hose  sell  at  $  5.75,  what 
do  125  ft.  sell  for? 

19.  When  asked  his  age,  a  man  replied,  "  f  of 
my  age  is  22|  years."     How  old  was  he  ? 

Suggestion 
1     J.  ,  .  .      45      8     J.  ...    45  X  8      m. 

8  "*  ^''  ^^'  ''  273'  8  "^  ''  ''  Y^-  ^^'" 
cancel. 

20.  If  8^  yd.  of  calico  cost  $.66,  what  will 
57  yd.  cost  ? 

21.  If  the  rent  for  a  house  for  9  mo.  was 
$319.50,  what  is  the  rent  for  a  year? 

22.  If  a  certain  sum  of  money  brings  $  198  in 
15  months,  what  will  it  bring  in  20  months  ? 

23.  If  65  %  of  a  certain  sum  of  money,  put  out 
at  interest,  yields  $  390  annually,  how  much  would 
the  entire  sum  yield  at  the  same  rate  of  interest  ? 

24.  At  $14.50  a  hundredweight,  what  will 
71  lb.  cost  ?     171  lb.  ? 

25.  If  5  men  can  do  a  piece  of  work  in  12  da., 
how  long  will  it  take  15  men  to  do  the  same 
work? 


176  INTERMEDIATE  BOOK 

Solution  and  Explanation 

Will  1  man  do  the  work  in  a  longer  or  a  shorter 
time  than  5  men?  To  find  the  time  it  takes 
1  man  to  do  the  work  must  you  multiply  12  days 
by  5,  or  divide  12  days  by  5  ? 

If  it  takes  1  man  12  x  5  days,  must  this  product 
be  multiplied  by  15  or  divided  by  15,  to  find  the 
time  it  takes  15  men  to  complete  the  work  ? 

26.  If  12  dredging  machines  can  clear  a  certain 
channel  in  18  days,  how  long  will  it  take  16  to  do 
the  same  work  ? 

27.  If  4  persons  eat  5  packages  of  breakfast 
food  in  15  days,  how  many  persons  will  eat 
6  packages  in  8  days  ? 

Solution  and  Explanation 

If  5  packages  are  eaten  in  15  da.  by  4  persons, 
then  5  packages  are  eaten  in  1  da.  by  4  x  15  per- 
sons ;  1  package  is  eaten  in  1  da.  by  — - —  persons ; 

5 

6  packages  are  eaten  in  1  da.  by per- 

5 

sons,   and    6    packages   are   eaten    in    8    da.    by 

6x4x15  c-        36x2x15     o   .u 

— - — - —  persons,     bmce  — - — - —  =  9,  the  an- 
5x8       ^  5x8  ' 

swer  is  9  persons. 

In  this  method  of  solution,  the  concrete  number 

of   the   kind   required  in   the  answer  is  put  last. 


SOLUTION  OF  PROBLEMS  177 

In  this  example,  the  required  number  is  "  persons." 
We  arrange  the  statement  so  that  "  persons  "  comes 
last. 

28.  If  2  launches  require  10  gallons  of  oil  to 
travel  7  hours,  how  many  launches  can  travel  on 
15  gallons  for  3  hours  ? 

29.  If  it  takes  2  boys  5  days  to  build  a  pigeon 
house,  how  long  will  it  take  3  boys  working  at  the 
same  rate  ? 

30.  If  880  bricks  are  needed  for  a  wall  10  ft. 
long,  2  ft.  wide,  and  2  ft.  high,  how  many  bricks 
are  needed  for  a  wall  12  ft.  long,  1  ft.  wide,  and 
5  ft.  high  ? 

31.  A  clothier  invests  $368.55  in  boys'  coats. 
How  many  does  he  buy,  if  each  coat  costs  $  1.89  ? 

32.  A  man  fails  in  business.  He  owes  $7900, 
and  his  creditors  receive  65%  of  this.  What 
amount  do  they  receive  ? 

33.  If  f  of  a  man's  money  is  $2430,  how  much 
has  he  ? 

34.  How  long  is  a  pole,  if  ^  of  it  is  40  ft.  ? 

35.  If  10  yd.  of  gingham  cost  $  .75,  how  much 
will  87  yd.  cost? 

36.  If  3  teams  of  horses  can  plow  a  field  in  1 6  days, 
how  long  will  it  take  4  teams  to  plow  the  same  field  ? 

37.  If  5  men  can  do  a  piece  of  work  in  12  days, 
how  long  will  it  take  7  men  to  do  the  same  work  ? 


178  INTERMEDIATE  BOOK 

38.  If  1.8  yd.  of  silk  cost  $3.24,  find  the  price 
of  71  yd. 

39.  The  earth  moves  in  its  path  around  the  sun 
at  the  rate  of  1110  miles  a  minute.  How  many 
times  faster  does  it  move  than  a  train  which  travels 
54  miles  an  hour  or miles  a  minute  ? 

40.  If  a  train  travels  75  miles  in  If  hours,  how 
far  will  it  travel  in  7  hours  ? 

41.  Skimming  milk  by  hand,  only  f  of  the  cream 
is  obtained.  In  a  week  a  farmer  obtained  270  qt. 
of  cream.  How  much  would  he  have  obtained  if 
he  had  used  a  separator,  which  extracts  all  the 
cream  ? 

42.  William  earns  $750  a  year,  which  is  f  as 
much  as  his  father  earns.  How  much  does  his 
father  earn  ? 

43.  If  ^j  of  a  certain  number  is  42,  how  much 
is  f  of  that  number  ? 

44.  If  a  stable  has  enough  oats  to  feed  30  horses 
45  days,  how  long  will  the  oats  feed  20  horses  ? 

45.  If  a  clock  gains  1|-  minutes  in  24  hours,  how 
much  time  will  it  gain  in  40  hours  ? 

46.  At  the  rate  of  3  miles  an  hour,  I  can  walk  a 
certain  distance  in  2  hours  30  minutes.  What  is 
my  rate  when  I  walk  this  distance  in  3  hours  ? 

47.  If  a  certain  weight  of  sheet  iron,  f  in.  thick, 
covers  45  sq.  ft.,  how  many  square  feet  will  the 
same  weight  of  sheet  iron  only  J  in.  thick  cover? 


SOLUTION  OF  PROBLEMS  179 

48.  Using  4  electric  lights,  the  electric  bill  is 
$  5  a  month.  What  is  the  bill  for  6  months  when 
3  electric  lights  are  used  ? 

49.  If  the  interest  on  a  certain  sum  of  money  is 
$  120  for  9  months,  what  is  the  interest  on  that 
sum  for  25  months  ? 

50.  A  farmer  raised  1,125  bushels  of  beets  on  3 
acres.  At  this  rate,  how  many  bushels  could  he 
have  raised  on  11  acres? 

Unitary  Analysis 

218.  1.  If  3  packages  of  rolled  oats  sell  for  24^, 
what  is  the  cost  of  4  packages  ? 

Analysis 

In  problems  of  this  kind  it  is  often  easier  to 
find  the  cost  of  one  unit,  then  the  cost  of  the 
required  units.  In  this  case  find  the  cost  of  1 
package,  then  the  cost  of  4.     Thus, 

If  3  packages  sell  for  24^, 

1  package  sells  for  ^  of  24^,  or  8^. 
4  packages  sell  for  4  x  8^  =  32^.     Ans. 

2.    If  276  is  f  of  a  number,  what  is  the  number  ? 

Analysis 

If  I  of  the  number  =  276,  then 

i  of  the  number  =  1  of  276  =  ^^=69. 
f  of  the  number  =  5  x  69  =  345.     Am, 


180  INTERMEDIATE    BOOK 

Oral  Exercise 
219.  Analyze,  explaining  the  process  in  each  case : 

1.  If  51  is  f  of  a  number,  what  is  the  number  ? 

2.  If  15  is  f  of  a  number,  what  is  the  number  ? 

3.  Of  what  number  is  12  the  six  sevenths  part  ? 

4.  54  is  ^Y  of  what  number  ? 

5.  56  is  ^  of  what  number  ? 

6.  If  48  is  f  of  a  number,  what  is  the  number  ? 

7.  If   121   is   ^-   of   a   number,   what   is   the 
number  ? 

8.  If  3  men  together  earn   $12  in  one  day, 
what  will  7  men  earn  daily  at  the  same  rate  ? 

9.  If  14  men  pay  $56  for  board  per  week, 
what  will  11  men  pay  at  the  same  rate  ? 

10.  If  4  yd.  cost  22^,  what  will  10  yd.  cost? 

11.  35  is  f  of  what  number  ? 

12.  27  is  f  of  what  number  ? 

13.  100  is  20  %  of  what  number  ? 

14.  21  is  1 J  times  what  number  ? 

15.  40  is  .20  of  what  number  ? 

16.  24  is  ^  less  than  what  number  ? 

17.  16  is  1^  less  than  what  number? 

18.  48  is  ^  more  than  what  number  ? 

19.  36  is  I'  more  than  what  number  ? 

20.  75  is  75  %  of  what  number  ? 


APPROXIMATIONS 

Oral  Exercise 

220.  As  a  check  against  absurd  results  it  is 
desirable  that  pupils  accustom  themselves  to  giving 
approximate  answers.  Whenever  possible,  the  ap- 
proximate results  should  be  found  orally.  Suppose 
a  pupil  wishes  to  find  the  cost  of  2.8  lb.  at  $  1.05  a 
pound  and  writes  his  answer  $  29.40.  By  a  brief 
mental  computation  he  should  detect  the  error  at 
once.  2.8  lb.  is  nearly  3  lb.,  and  $  1.05  is  nearly 
$  1.  3  lb.  at  $  1.00  gives  $  3.00  as  an  approximate 
answer.  Hence,  $29.40  is  absurd.  The  correct 
answer  is  $  2.94. 

221.  Give  the  approximate  answer.  Check  with 
the  correct  answer. 

1.  28  handkerchiefs  at  $  .24. 

2.  22  yards  at  $.29. 

3.  13  wool  blankets  at  $4.95.. 

4.  5  gingham  skirts  at  $  .98. 

5.  11  suits  of  clothes  at  $12.75. 

6.  98  yd.  of  silk  at  $  .79. 

7.  Find  cost  of  1  pair  of  shoes  when  15  pairs 
cost  $  74.25. 

181 


182  INTERMEDIATE  BOOK 

8.  Cost  of  23  linen  suits  at  $  3.98  each. 

9.  Cost  of  105  pairs  of  shoes  at  $  2.45  a  pair. 

10.  At  44 1^  a  pound,  find  cost  of  2|-  lb. 

11.  Cost  of  1  hammock,  31  cost  $96.72. 

12.  The  monthly  salary  of  a  man  who  receives 
$  2350  a  year. 

13.  Cost  of  52  books  of  fiction  at  $  .39. 

14.  Cost  of  19  sacks  of  potatoes  at  $  1.25. 

15.  Suggest  problems  for  testing  the  ability  to 
estimate  answers  that  are  approximately  correct. 


AVERAGES 

Introduction 

222.  We   have   used   the  term  average   in  our 

problems  and  our  discussions. 

The  average  of   6,   7,   11   is  found  by  adding 

them  and  dividing  the  sum  by  3. 

mi,                  •    6+7-fll     24     Q 
Ihe  average  is =  -—  =  8. 

3  3 

In  all  cases,  find  the  total  of  the  items,  then 
divide  the  sum  by  the  number  of  the  items. 

Statistics  are,  to  a  large  extent,  averages. 

We  speak  of  the  average  attendance  at  school, 
the  average  temperature,  the  average  number  of 
days  of  sunshine  per  month,  the  average  rations 
for  man  and  animals,  the  average  height  of  men, 
the  average  crop,  and  so  on. 

What  problem  can  you  make  requiring  that  the 
average  be  found  ? 

Problems  in  Averages 

223.  1.  John  is  11  years  old,  James  12,  Harry 
10,  Wallace  15.     Find  the  average  age. 

2.  A  driver  earned  on  successive  days  $  3,  $  5, 
$4,  $  1.     What  is  his  average  daily  earnings  ? 

183 


184  INTERMEDIATE  BOOK 

3.  A  merchant's  receipts  for  3  consecutive  days 
were  $  200,  $  200,  $  500.  Find  his  average  daily 
receipts. 

4.  At  6  o'clock  on  4  mornings  the  thermometer 
stood  61°,  59°,  50°,  70°.  Find  the  average  tem- 
perature. 

5.  A  man  earns  50  j^  an  hour.  He  works  6  hr. 
on  Monday,  2  on  Tuesday,  7  on  Wednesday,  10  on 
Thursday,  8  on  Friday  and  3  on  Saturday.  What 
were  his  average  daily  earnings  ? 

Written  Problems 

224.  1.  What  is  the  average  weight  of  5  bales 
of  cotton  weighing  450,  460,  475,  455,  457  lb.? 

2.  What  should  ground  feed,  made  from  an 
equal  number  of  bushels  of  oats  @  28^,  barley 
@  78^,  and  corn  @  59^,  be  sold  per  bushel,  in 
order  to  yield  a  profit  of  20  %  on  the  cost  ? 

3.  The  weekly  salary  list  of  5  employees  in  a 
store  is  $  25,  $  20,  $  18,  $  17.75,  $  15.50.  What  is 
the  average  weekly  salary  ? 

4.  The  cyclometer  on  an  automobile  shows  that 
the  distances  traveled  in  4  da.  are  130.4  mi.,  82.27 
mi.,  90.01  mi.,  207.54  mi.  What  is  the  average 
distance  traveled  per  day  ? 

5.  A  pleasure  launch  uses  5J  gal.  gasoline  the 
first  day,  4|-  gal.  the  second  day,  6|-  the  third  day. 


SOLUTION  OF  PROBLEMS 


185 


and  4|-  the  fourth  day.     What  is  the  average  daily 
consumption  of  gasoline  ? 


225. 

Table 

FOR  Reference 

Height 

Ages 

Ft. 

In. 

15-24 

2^29 

30-34 

85-39 

40-44 

45-49 

50-54 

lb. 

lb. 

lb. 

lb. 

lb. 

lb. 

lb. 

5 

0 

120 

125 

128 

131 

133 

134 

134 

5 

2 

124 

128 

131 

133 

136 

138 

138 

5 

4 

131 

135 

138 

140 

143 

144 

145 

5 

6 

138 

142 

145 

147 

150 

151 

153 

5 

8 

146 

151 

154 

157 

160 

161 

163 

5 

10 

154 

159 

164 

167 

170 

171 

172 

6 

00 

165 

170 

175 

179 

180 

183 

182 

226. 


Problems  Based  on  the  Table 

1.    The  weights  given  in  this  table  are  the 


averages  obtained  by  weighing  74,162  applicants 
for  life  insurance.  From  this  table  complete  the 
average  weight  of  men  between  the  ages  of  15  and 
24,  which  are  not  less  than  5  ft.  nor  more  than 
6  ft.  tall. 

2.  Do  the  same  for  each  of  the  six  other  age 
periods  in  the  table. 

3.  Find  the  average  weight  of  men  5  ft.  tall, 
between  the  ages  of  15  and  54  years. 

4.  Do  the  same  for  each  of  the  other  heights 
given  in  the  table. 

5.  Make  5  problems  based  on  the  table. 


THE   DIRECT   METHOD    OF    SOLUTION 

227.  It  frequently  happens  that  the  solution  of 
problems  may  be  performed  in  a  direct  method  by 
eliminating  useless  operations.  The  results  are 
more  speedily  obtained  in  this  way  and  there  is  less 
likelihood  of  error. 

Oral  Problems 

1.  If  butter  sells  at  $  18.50  per  100  lb.,  what 
is  the  cost  of  300  1b.? 

Solution.  —  In  examples  like  this,  where  300  lb.  is 
exactly  divisible  by  100  lb.,  it  is  easier  not  to  find  the 
cost  of  1  lb.  Since  300  lb.  is  3  times  100  lb.,  the  cost 
of  300  lb.  will  be  3  times  118.50,  or  8  55.50.  This 
is  called  the  direct  method  of  solution, 

2.  At  $3.50  for  200  lb.  of  lignite,  what  is  the 
cost  of  6000  1b.? 

3.  Find  the  cost  of  120  eggs  at  23|^  per  dozen. 

4.  Find  the  cost  of  300  bbl.  of  flour  at  $  575  a 
100  bbl. 

5.  If  10  men  earn  %  175  a  week,  what  will  40 
men  earn  in  the  same  time  ? 

6.  If  10  men  can  do  a  piece  of  work  in  36  days, 
how  long  will  it  take  40  men  to  do  the  work  ? 

7.  How  much  will  150  gal.  of  molasses  cost  at 
$12.50  for  50  gal.? 

186 


THE  DIRECT  METHOD  OF  SOLUTION        187 

8.  Mary  bought  10  yd.  of  cheviot  at  $3.95.  If 
Lucy  bought  30  yd.  of  cheviot,  how  much  did  she 
pay  ? 

Written  Problems 

228.  Solve,  using  direct  method  wherever  pos- 
sible : 

1.  In  a  city  of  200,000  inhabitants,  93  inhabi- 
tants out  of  every  1000  are  foreign  born.  What  is 
the  total  foreign  population  ? 

2.  In  the  same  city  there  are  2|-  grocery  stores 
for  every  6  inhabitants,  or  how  many  grocery  stores 
in  all? 

3.  If  a  circle,  16  in.  in  diameter,  has  a  circum- 
ference of  50.2  in.,  what  is  the  circumference  of 
a  circle  whose  diameter  is  112  in.? 

4.  If  56  lb.  of  rye  make  a  bushel,  how  many 
bushels  in  1120  1b.? 

5.  What  will  8000  bu.  of  barley  weigh,  if  40  bu. 
weigh  1920  lb.  ? 

6.  If  1  cu.  ft.  of  cast  iron  weighs  446  lb.,  what 
will  144  cu.  in.  weigh  ? 

7.  What  is  the  cost  of  floor  tiles  for  a  room 
35  ft.  by  40  ft.,  at  $  15  per  100  sq.  ft.  ? 

8.  A  certain  mantel  tiling  costs  40^  per  square 
foot.  If  a  man  purchases  tiling  to  the  amount  of 
$  8,  how  many  square  feet  can  he  cover  ? 


188 


INTERMEDIATE  BOOK 


Oral  Exercise 
229.    Find  the  cost : 


Articles 

Kate 

Articles 

Rate 

Articles 

Rate 

1.       7 

Si0Tl2f 

5 

2  for  24^ 

6 

5  cost  55^ 

2.     10 

4  for  20^ 

6 

7  cost  Mf 

3 

4  cost  52  ^ 

3.       3 

2  cost  34^ 

2 

3  cost  27  ^ 

12 

7  cost  28  J^ 

4.     30 

331  cost  100^ 

12 

12^  cost  100^ 

6 

16|  cost  100^ 

5.       6 

4  cost  32^ 

5 

6  cost  72^ 

21 

30  cost  60  ^ 

6.       5 

3  cost  36  J? 

9 

5  cost  75^ 

10 

4  cost  36  ^ 

7.     12 

4  cost  $44 

7 

6  cost  $36 

100 

2  cost  $3.50 

8.    100 

3  cost  $3.60 

100 

7  cost  $2.10 

100 

5  cost  $5.50 

9.     20 

13  for  $2.60 

200 

14  for  $4.20 

30 

11  for  $1.21 

10.     50 

6  for  15^ 

10 

6  for  $4.20 

4 

3  for  $3.30 

PROBLEMS    THAT    MAY    BE    ILLUSTRATED    BY 
SIMPLE   GRAPHS 

Industry 

230.  1.  Much  gold  and  silver  is  taken  from 
mines  in  Colorado,  California,  and  Nevada.  Coal 
is  found  in  many  places  in  the  United  States.  Is 
the  coal  taken  out  of  the  earth  in  one  year  worth 
as  much  as  the  gold  and  silver  ?  The  lines  show 
the  value  of  several  minerals  produced  in  the 
United  States  during  one  year.  One  inch  stands 
for  120  million  dollars.  Which  mineral  repre- 
sents the  greatest  value  ?  Which  the  least  ?  How 
long  is  the  line  representing  soft  coal  ?  Measure 
the  line  to  the  nearest  tenth  of  an  inch  and  see 
how  nearly  correct  you  are. 

Soft  Coal ,  

Gold  &  Silver 

Hard  Coal 

Iron _— ^__--. 

Copper.. _____-■_ 

2.  How  many  million  dollars  stand  for  the 
value  of  the  soft  coal  for  last  year  ? 

3.  How  long  is  the  line  for  gold  and  silver,  and 
how  many  million  dollars  does  it  represent  ? 

4.  How  many  million  dollars  of  hard  coal  were 
produced? 

189 


190  INTERMEDUTE  BOOK 

5.  How   many  millions   more    soft   coal   than 
hard  coal  ? 

6.  How  many  millions  more  of  soft  coal  than 
gold  and  silver  ? 

7.  About  how  much  more  of  gold  and  silver 
than  hard  coal  ? 

8.  How    many    million    dollars    of    iron    were 
mined? 

9.  How  many  million  dollars  of  copper  were 
mined  ? 

10.  The  limestone  production  was  valued  at  30 
million  dollars  How  long  a  line  stands  for  that 
value  ? 

11.  Draw  a  line  representing  a  mineral  produc- 
tion worth  150  million  dollars. 

12.  Construct  similar  problems  of  your  own. 

Rainfall 

231.  1.  The  United  States  government  has 
gauges  in  different  parts  of  the  country  by  which 
the  exact  amount  of  rain  or  melted  snow  is  meas- 
ured. From  this  diagram,  show  during  which  two 
months  San  Francisco  has  the  least  rain  and  Santa 
Fe  the  most. 

2.    During  which  months  has  San  Francisco  the 
most  rain  and  Santa  Fe  the  least  ? 


PROBLEMS  THAT  MAY  BE  ILLUSTRATED      191 


3.  On  a  strip  of  paper  copy  carefully  the  scale 
of  inches. 

You  can  measure  easily  to  the  nearest  J  of  an 
inch  or,  if  you  are  careful,  to  the  nearest  ^  of  an 

Normal  Monthly  Rainfall 


m 
SAN  FRANCISCO 
GAL. 


1 


in 

SANTA  fE 

N.  MEX. 


Jj 


>.  g  ^  bb 


m  O 


O      0) 

"A  P 


inch.     If  you  apply  the  scale  to  the  line  showing 

the  rainfall  in  San  Francisco  for  January,  you  find 

the  line  4|^  in.  Ions;.  c?    i     *  t    v 

*>  ^  ,  Scale  of  Inches 

That  means  that  if  a  tub  12      3      4       5 

is  left  out  of  doors  to  catch 
the  rain  and  snow  during 
January,  the  rain  and  melted  snow  in  the  tub  at 
the  end  of  the  month  is,  in  an  average  year,  4|  in. 
deep. 

The  tub  must  not  leak.     It  must  be  covered 
during  fine  weather,  to  prevent  evaporation. 

4.    Find  the  number  of  inches  of  rainfall  for  a 
year  in  San  Francisco.     Also  in  Santa  Fe. 


192  INTERMEDIATE  BOOK 

5.  In  whicli  place  is  the  total  amount  of  rain- 
fall for  one  year  greater  ? 

6.  Which  place  has  a  more  even  distribution  of 
the  rainfall  throughout  the  year  ? 

7.  In  which  place  can  you  more  easily  dispense 
with  an  umbrella  during  a  summer  vacation  ? 

8.  During  6  successive  years  in  Santa  Fe  the 
number  of  inches  of  rainfall  per  year  was  20,  14, 
20,  12,  10,  16.     Find  the  average. 

9.  In  some  parts  of  the  Panama  Canal  zone  the 
annual  rainfall  is  as  high  as  120  in.  How  many 
times  more  is  this  than  15  in.,  which  is  the  annual 
rainfall  in  Denver  ? 

10.  At  Cheyenne,  Wyo.,  the  monthly  rainfall 
(in  inches),  beginning  with  January,  is  as  follows : 

4         5         8       1    5       9,  4       1    5       9,     1    5         9         7         4         3 
TO"?  TO"'  TO"?   -'-ro'?  ^10"?   -*^T0"'  ^?   -*-T0?    10?  TO"?  TO?  TO* 

Find    the    rainfall    per    year,    also    the    monthly 
average. 

Population  of  the  United  States 

232.  1.  The  curve  AB  shows  the  increase  in 
population  in  the  United  States  during  110  years. 
Years  are  marked  off  from  left  to  right ;  the  popu- 
lation from  the  bottom  line  up.  One  space  up 
stands  for  5  million  inhabitants.  The  point  A 
indicates  the  population  in  the  year  1800.  This 
point  is  about  one  space  up  and  stands,  in  round 
numbers,  for  how  many  inhabitants  ? 


PROBLEMS  THAT  MAY  BE  ILLUSTRATED    193 


CO 


o 

CO 
00 


o  o 

O     y-i 
05     05 


90 


80 


s  70 


60 


2.  At  the  year  1820  the  curve  is spaces  up. 

This  indicates  about inhabitants. 

3.  At  the  year  1840  the  curve  is  a  little  more 
than  3  spaces  up,  or  about  3.4  spaces.  The  popu- 
lation was,  there- 
fore, about  3  4 
times  5  million, 
or million. 

4.  In  this  way 
estimate  the  pop- 
ulation for  1860, 
1880,  1900,  and 
1910. 

5.  About  how 
many  more  in- 
habitants were 
there  in  1820 
than  in  1800? 
In  1900  than  in 
1880? 

6.  Estimate 
the  population 
for     the     years 

1810,  1830,  1850,  1870,  and  1890. 

7.  Make  a  new  graph  to  show  about  what  the 
population  of  the  United  States  is  in  1915.  What 
will  be  the  approximate  population  of  the  United 
States  in  1920  ? 


-)  50 


'^  40 


30 

20 

10 
A 


"1 

B 

/ 

/ 

/ 

1 

/ 

/ 

f 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

/ 

X 

1 

194 


INTERMEDIATE  BOOK 


The  Money  Value  of  Training 

233.  The  St.  Nicholas  (Vol.  31,  p.  57)  gives 
statistics  of  two  typical  boys.  The  wages  of  John, 
who  enters  a  shop  at  the  age  of  16,  are  compared 


^ 

y 

y 

$20 

/ 

/ 

>r     J 

/^ 

yi.<y 

S$15 

^ ' 

''^ 

^ 



y 

^ 

1^ 

y 

^■s, 

[^ 

^1 

y 

X^O^ 

n, 

• 

If^"" 

• 

/ 

& 

^■^ 

^ 

^ 

.^ 

$5 

^^ 

^'1 

^y'^ 

16   17   18   19   20   21   22   23  24  25  26 
Ages  in  Years 

with  the  wages  of  Jack,  who  at  the  age  of  16  goes 
to  a  trade  school  for  3  years'  training,  and  then 
enters  a  shop.  The  dotted  line  shows  John's 
wages ;  the  full  line  shows  Jack's  wages. 

1.  How  much  does  John  earn  weekly  when  he 
is  16  years  old  ?  When  he  is  17  ?  When  he  is 
18  ?  Each  space  from  the  lowest  line  up  stands 
for  1.  When  John  is  16  years  old,  the  dotted  line 
is  3  spaces  up.     His  weekly  wages  are  then  %  3. 


PROBLEMS  THAT  MAY  BE  ILLUSTRATED    195 

2.  Does  Jack  earn  anything  when  he  is  16,  17, 
18  years  old  ? 

3.  At  the  age  of  19,  how  much  does  each  earn  ? 
How  much  more  does  Jack  earn  ? 

4.  At  the  age  of  20,  how  much  does  each  earn  ? 
Find  the  difference  in  their  wages. 

5.  At  what  age  are  John's  wages  more  nearly 
equal  those  of  Jack  ? 

6.  At  what  age  does  John  reach  his  highest 
wage? 

7.  Do  Jack's  wages  steadily  increase  ? 

8.  At  what  age  does  John  earn  as  much   as 
Jack  earns  at  19  ? 

9.  At  what  age  does  Jack  earn  as  much   as 
John  earns  at  24  ? 

10.    Does  John  ever  earn  as  much  as  Jack  does 
at  the  age  of  21^? 


PART   TWO 


PERCENTAGE 

Introduction 

234.   When  we  say  that  5  per  cent  of  the  enrolled 

pupils  are  absent, 
we  mean  that  5  out 
of  every  100  pupils, 
or  5  hundredths  of 
them,  are  absent. 

Per  cent  means 
hundredths. 

Five  per  cent  is 
written  5  %.  It 
means  5  hundredths^ 
or  3-|o,  or  .05. 

1.    If  a  school  has 
200  pupils  enrolled, 
and  4  %  are  absent,  what  is  the  number  of  pupils 
that  are  absent  ? 

4  %  means  j^,  or  .04. 

To  find  4  %  of  200  we  multiply  200  by  3^^,  or  .04. 

We  have  200  x  .04  =  8,  the  answer. 

2.    How  many  little  squares  are  there  in   this 
drawing  ?     Shade  3  %  of  them.     Shade  6  % ;  8  %. 

196 


In  this  Illustration  1  %  op  the  Sur- 
face 18  Shaded 


PERCENTAGE  197 

3.  How  many  squares  must  be  shaded  to  make 
them  25  %  of  the  whole  ? 

4.  How  much  is 

^loOflOO?  1%  of  100? 

3;|oofl00?  2%  of  100? 

^  of  100?  5%  of  100? 

^J^  of  200?  1%  of  200? 

3-|oof200?  2%  of  200? 

1^  of  500?  4%  of  500? 

^  of  800?  6%  of  800? 

^  of  1000?  8%  of  1000? 

5.  Study  and  compare 

a.   ^f^=.05  =  5%  &.   3;fo  =  .04  =  4% 

c.    3-f^=.06  =  6%  d.   ^=.08  =  8% 

e,    J^=.12  =  12%  /   3^=. 20  =  20% 


Reduction  of  Decimals  and  Common  Fractions  to 
Per  Cents 

235.   Express  with  the  per  cent  sign : 

1.  .06. 

Process 

.06  =  ^^0  =  6% 

2.  .05       3.   .07       4.    .09        5.    .04       6.    .02 

7.     .1  8.     .11  9.     .12        10.     .13        11.     .14 

12.   .20      13.    .30      14.    .40      15.    .50      16.    .80 
Tell  how  to  express  a  decimal  as  a  per  cent. 


198  INTERMEDIATE  BOOK 

Written  Exercise 

236.  Express  with  the  per  cent  sign : 

1-  ^- 

Process 

A=t'A=60% 

^'    Th        3-    TTO         4-    tA        5.     ^  6. 

^-    TTT         ®-    TFO  ^-    TFO       ^^'    TO        ^^• 

12.     1^         13.     1^       14.     3^2_       15.     _^        16, 
17.    _^        18.     ^^       19.    ^SL         20.    3^     21.     ^^ 

Tell  how  to  express  a  common   fraction  as   a 
decimal. 

Written  Exercise 

237.  Express  as  a  decimal : 

1.    8%. 

Process 

8%  =^  =  .08 


6 
100 

_5_ 
100 


2.    10%         3. 

9%        4.  7% 

5. 

6% 

6. 

5% 

7.    2%            8. 

1%        9.  20% 

10. 

30% 

11. 

40% 

12.    50%       13. 

80%     14.  25% 

15. 

75% 

16. 

66% 

TeU  how  tc 

>  express  per  cent 

as  a  decimal. 

Written  Exercise 

238.    Write 

as  common  fractions 

i  in  their  lowest 

terms  : 

1.    10%. 

Process 

tV 

PERCENTAGE 


199 


2.     6%  3.     4%         4.     12%       5.     16%         6.     18% 

7.   20%     8.   25%     9.   50%   10.   40%     ii.   75% 
12.   48%    13.   64%  14.   24%   15.    72%     is.   96% 


Drill  Exercise 
239.   Memorize  these  relations  : 


50%  =  J 

100%  =  1 

331%=!=. 33^ 

25%  =  J 

75%  =1 

66|%=f  =  .66| 

20%  =1 

10%  =  ^ 

12i%=i=.12i 

2%=^V 

62J%  =  | 

37J%  =  |=.37i 

iro=jh 

80%  =  f 

16|%=i=.16f 

Written  Exercise 

240.   Write  as  common  fractions  in  their  lowest 
terms  : 


1.  121 


2.  331% 


Process 
121%  =  .121  =  1 


3.  66t 


371% 


871% 


Comparison 

241.  1.  How  many  fifths  of 
AisBI  (7?  D?  Ul 

2.    How  many  hundredths 
of^is^?    Z)?     (7?  B1 

3.    What  per  cent  of  A  is 
(7?   ^?   i)?   ^? 

4.   What  per  cent  of  Z)  is  ^? 


A    B 


D      E 


200  INTERMEDIATE  BOOK 


5.  What  per  cent  oi  Cis  JEI   Z)? 

6.  What  per  cent  of  ^  is  J5' ?   i)?    (7? 

7.  What  part  is  50  %  of  J.  ?     20  %  of  J.  ? 

8.  What  part  is  50  %  of  ^  ?     25  %  of  ^  ? 

.    9.  What  part  is  331%  of  CI     66f  %  of  (7? 

10.  What  part  is  50  %  of  i)  ?     100  %  of  i)  ? 

Oral  Exercise 

242.  1.  How  many  hundredths  of  an  inch  is  | 
in.?  fin.?  fin.?  fin.?  fin.?  fin.?  fin.? 
fin.? 

2.  What  per  cent  of    1  in.  is  f  in.  ?      f  in.  ? 
fin.?     fin.?     fin.?     fin.?     fin.?     fin.? 

3.  What  per  cent  of  2  ft.  are  6  in.  ?     3  in.  ? 
2  in.  ?     1  in.  ?     4  in.  ?     5  in.  ?     9  in.  ? 

4.  What  part  of  1  inch  is  50  %  of  it  ?     25  %  of 
1  inch  ? 

5.  What  part  of  J  an  inch  is  25  %  of  it  ?     50  % 
of!  inch? 

Study  Exercise 

243.  Consider  the  exercise  5  %  of  400  is  20. 

In  this  exercise  we  call  400,  the  base;  5%,  the 
rate ;  and  20,  the  percentage. 

The  number  upon  which  the  percentage  is  found 
is  called  the  base. 

The  number  of  hundredths  to  be  taken  is  called 
the  rate  or  rate  per  cent. 


PERCENTAGE  201 

The  result  obtained  by  finding  a  certain  per  cent 
of  the  base  is  called  percentage. 

When  you  have  the  product  of  two  numbers, 
how  do  you  check  your  result  ? 

If  you  divide  the  percentage  by  the  base,  what  is 
the  quotient  ? 

Or,  if  you  divide  the  percentage  by  the  rate 
(expressed  decimally),  what  is  the  quotient  ? 

We  have,  therefore,  the  following  principles : 

The  percentage  is  equal  to  the  base  multiplied  by 
the  rate. 

The  rate  is  equal  to  th*e  percentage  divided  by 
the  base. 

The  base  is  equal  to  the  percentage  divided  by 
the  rate. 

1.  Given  the  base  $  2300,  the  rate  8  %,  compute 
the  percentage. 

2.  Given  the  rate  11%,  the  base  3587  lb.,  find 
the  percentage. 

3.  When  you  know  the  base  and  the  rate,  how 
do  you  find  the  percentage  ? 


If  we  write  h  for  base,  r  for  rate, 
percentage,   we   can    indicate   these 
more  briefly  by  means  of  equations  oi 
thus, 

and  p  for 

principles 

•  formulas. 

p  =  hxr, 

h            r 

202  INTERMEDIATE  BOOK 

Find  the  Percentage 

Written  Exercise 

244.   1.   Find  5  %  of  100  bu. 

Explanation.  — 

Apply    the    formula 

Process  p  =  h  x  r.       Change 

5  %  of  100  bu.  =  Yo"^  of  100  bu.    the  per  cent  into  a 

=  100x-^-  decimal  fraction. 

_  g  ^^^  The    exercise     then 

becomes  an  exercise 

in   fractions.     Solve 

by  fractions. 

In  the  exercise  what  is  the  base  ?  What  is  the 
rate  ?  What  is  the  percentage  ?  Perform  the 
operation  by  fractions  when  it  is  possible  to  do  so 
to  advantage. 


2. 

Find  5%  of  600  1b. 

3.    6  %  of  50  yd. 

4. 

20  %  of  60  oz. 

5.    30  %  of  400  bu. 

6. 

12%  of  900doz. 

7.    3  %  of  800  mi. 

8. 

5%  of  80^. 

9.    16%  of  20T. 

10.    50^ 

7  of  40  men. 

Written  Exercise 

245.   Apply  the  formula.     Solve  and  explain. 

Find  6  %  of : 

100     400    150    250    300 
200    1000    900    500    700 


PERCENTAGE  203 

Find  8  %  of  each  of  the  following : 


200    700 

900 

150 

250 

450    500 

550 

600 

750 

What  is  10%  of: 

350  A.    130  T. 

145  bu. 

700  men 

870  bu. 

750  bricks  930  ft. 

670  lambs 

360  da. 

750  ft. 

Written  Problems 

246.  Read  the  problems  carefully.  Select  the 
formula  to  be  used.  Decide  whether  to  use  frac- 
tions or  decimals  in  the  solution.  Then  solve  the 
problem. 

1.  A  farmer  has  200  sheep,  of  which  5  out  of 
every  hundred,  or  5  %,  are  black.  How  many  sheep 
are  black  ? 

In  this  problem  it  is  required  to  find  a  per  cent 
of  a  number.  What  is  the  base  ?  What  is  the 
rate  ?     What  is  the  formula  to  be  used  ? 

Process 

2.  John  buys  a  $2.50  hat  at  10%  off.  How 
much  does  he  save  by  this  reduction  in  price  ? 


204 


INTERMEDIATE  BOOK 


Process  by  Common 
Fractions 

10%  of  $2.50  =  J^  of  $2.50 
=  $21x33^ 

2    i^ 

2 

4 

=  $.25 


Explanation.  — 
Change  the  per  cent 
to  a  common  fraction. 
Change  the  number 
of  dollars  to  an 
improper  fraction. 
Multiply,  using  can- 
celation. Express 
the  fraction  of  a  dol- 
lar in  cents. 


Process  by  Decimals 

10%  of  $2.50  =  .10  of  $2.50 
=  $2.50x.l0 

=  $.25 


Explanation.  — 
Change  the  per  cent 
to  a  decimal  fraction. 
Multiply  as  in  deci- 
mals. 


Written  Problems 

247.  1.  A  suit  of  clothes,  marked  $15.50,  is 
sold  at  10  %  off.  How  much  in  dollars  and  cents 
was  saved  by  the  buyer  ? 

2.  A  merchant  offers  a  reduction  of  15  %  for 
cash  purchases.  Mary's  mother  buys  goods  to  the 
amount  of  $  150.  How  much  does  she  save  by 
paying  cash  ?     How  much  does  she  actually  pay  ? 

3.  A  school  has  360  pupils  enrolled.  Of  these 
5  %  are  absent.  How  many  pupils  are  absent  ? 
How  many  are  present  ? 


PERCENTAGE  205 

4.  A  man  sold  a  bicycle  that  cost  him  $  60,  and 
lost  15  %  of  the  cost.    What  was  the  selling  price  ? 

5.  Last  year  a  man  earned  $  1500.  This  year 
he  earned  8  %  more.  How  much  more  does  he  earn 
this  year  than  last  ? 

6.  An  agent  sells  a  lot  for  $1250  and  receives 
2  %  of  this  sum  for  selling  it.  How  much  does  he 
receive  ? 

7.  A  real  estate  man  bought  a  house  for  $  5750 
and  then  sold  it  at  a  profit  of  6  % .  What  was  the 
selling  price  ? 

8.  A  farmer  buys  32  cows  at  $55  each.  For 
what  sum  must  he  sell  his  stock  to  realize  10  %  on 
the  sum  paid  ? 

9.  A  boy  bought  a  bicycle  for  $  25  and  sold  it 
at  a  loss  of  40  % .     How  much  did  he  lose  ? 

10.  A  ranchman  lost  5%  of  his  herd  of  4560 
sheep.     How  many  sheep  were  left  ? 

11.  A  farm  costing  $  6000  was  sold  at  a  gain  of 
7  %.     What  was  the  amount  gained  ? 

12.  An  orchard  has  8  rows  of  trees  with  10  trees 
in  each  row.  Five  per  cent  of  the  trees  are  dead. 
How  many  trees  are  alive  ? 

13.  At  a  city  election  there  were  cast  5600  votes, 
of  which  the  successful  candidate  received  59  %. 
How  many  votes  did  he  receive  ? 


206 


INTERMEDIATE  BOOK 


Written  Exercise 

248.  1.   Find  36%  of  $32.50.    Check  the  answer. 

Process 

32.50 
.36 


19500 
97500 


Explanation.— 36%  =  .36. 
Hence,  36%  of  $32.50  is  the 
same  as  .36  off  32.50,  or  .36  x 
132.50  =  $11.70,  the  answer. 


11.7000 
Check:  1170 -^  36  =  32.50 


2. 

15%  of  $279.60 

3.    75  %  of  $  988 

4. 

161%  of  $960 

5.    12%  of  $304 

6. 

7  %  of  $  1234 

7.   371%  of  $875.50 

8. 

24|%  of  $1758.97 

9.   871%  of  $565.50 

10.   3i-%  of  $75.60 

Find  the 

Rate 

Written  Exercise 

249.   1.    If  the  base  is  $  375  and  the  percentage 
$52.50,  find  the  rate. 
Process 


.14 


375)52.50 
37  5 
15  00 
15  00 
.14  =  ^1^=14%     Am. 


Explanation.  —  Apply 
the  formula  r  =p  -i-b. 

Write  the  quotient  as  a 
per  cent. 


PERCENTAGE  207 

Find  the  rate : 

2.  Base  $83.40,  percentage  $4.17. 

3.  Base  $66,  percentage  $4.62. 

4.  Base  $  37.50,  percentage  $  13.50. 

5.  Percentage  540  lb.,  base  4500  lb. 

6.  Percentage  5.88  bu.,  base  36.75  bu. 

7.  Percentage  559.5  mi.,  base  746  mi. 

8.  Percentage  $  882,  base  $  840. 

Written  Problems 
250.    Use  pencil  only  when  necessary. 

1.  Herbert  writes  200  words,  but  misspells  20 
of  them.     What  per  cent  does  he  miss  ? 

The  problem  is  to  find  what  per  cent  one  num- 
ber is  of  another.  What  is  the  base  ?  What  is 
the  percentage  ?     What  formula  to  be  used  ? 

Process 

2.  A  fruit  raiser  planted  200  orange  trees,  7  % 
of  which  died.  How  many  trees  died  ?  Which  is 
the  base  ?  Which  the  rate  ?  Which  the  percent- 
age? 

3.  A  fruit  raiser  planted  200  orange  trees,  14 
of  which  died.     What  per  cent  died  ? 

4.  Of  300  children  enrolled  in  a  school,  5  %  are 
absent.     How  many  are  absent  ? 


208  INTERMEDUTE  BOOK 

5.  From  Problem  3  make  up  an  example  in 
which  the  base  and  the  percentage  are  given,  and 
the  rate  is  to  be  found. 

6.  With  the  numbers  $  500  and  5  %,  make  up 
a  problem,  to  find  the  percentage ;  then  a  problem 
to  find  the  rate. 

7.  A  boy  had  200  stamps,  but  lost  6.  What 
per  cent  did  he  lose  ?  In  other  words,  6  is  what 
per  cent  of  200  ? 

8.  The  loss  in  weight  of  800  lb.  of  wheat  in 
drying  was  16  lb.  What  was  the  rate  of  shrink- 
age? 

9.  A  small  army  of  600  men  has  66  officers. 
What  per  cent  of  the  army  are  officers  ? 

10.  A  tank  filled  with  2500  lb.  of  salt  water 
taken  from  Great  Salt  Lake  contains  475  lb.  of 
salt.  What  per  cent  of  salt  is  there  in  the  lake 
water  ? 

11.  5000  lb.  of  water  from  the  Atlantic  Ocean 
contains  180  lb.  of  salt.  What  per  cent  of  salt  is 
there  in  the  water  ? 

12.  A  man  at  the  seashore  allows  6600  lb.  of 
salt  water  to  evaporate  and  he  finds  that  264  lb.  of 
salt  remain  behind.  What  per  cent  of  salt  is 
there  in  the  water  ? 

13.  A  man  with  a  yearly  salary  of  $  1500  spends 
$112.50  on  clothes.  What  rate  per  cent  of  his 
salary  is  thus  spent  ? 


PERCENTAGE 


209 


Find  the  Base 

251.   1.    If  the  percentage  is  $  122.45  and  the  rate 
16  %,  what  is  the  base  ? 

Process 

$  765.31+ J.71S. 


,16)$  122.45.00 
112 


104 
96 


85 
80 


50 
48 
20 
16 
Check  the  answer  thus : 
$  765.31  X. 16  =  ? 


Explanation.  —  Apply 
the  formula  h  =  p-T-r. 
Change  16%  to  .16  and 
multiply  both  dividend  and 
divisor  by  100  in  order  to 
remove  the  decimal  point 
from  the  divisor.  This 
multiplication  may  easily 
be  performed  by  moving 
the  point  two  places  to  the 
right.     Why  ?     Check. 


Find  the  base  : 

2.  Percentage  80.75  T.,  rate  17  %. 

3.  Rate  6^  %,  percentage  32.5. 

4.  Rate  5|-  %,  percentage  41.47. 

5.  Rate  23  %,  percentage  107.18  lb. 

6.  Rate  .06,  percentage  $  30. 

7.  Percentage  11.4,  rate  .12. 

8.  Percentage  1139.45,  rate  3^. 


210  INTERMEDIATE  BOOK 

Written  Problems 
252.   1.    Mr.  Jones  borrows  $  400  and  pays  6  % 
interest  a  year.     How  much  interest  does  he  pay 
yearly  ? 

2.  Mr.  Jones  pays  $24.  interest  a  year,  which 
is  6  %  of  the  money  he  borrowed.  How  much  did 
he  borrow  ? 

Suggestion 

$  24 -f- .06  =  $400 

3.  How  many  pupils  in  a  school  of  200  pupils 
are  absent  if  3  %  are  absent  ? 

4.  From  Problem  3  make  an  example  in  which 
the  percentage  and  the  rate  are  given,  and  the  base 
is  to  be  found. 

5.  A  man  paid  $  18  interest  a  year,  which  was 
6  %  on  the  money  borrowed.  How  much  did  he 
borrow  ? 

6.  If  6  %  of  a  number  is  24,  what  is  the  number  ? 

7.  A  merchant  sold  a  motorcycle  for  80  %  of 
its  cost  and  received  $  160.  How  much  did  the 
machine  cost  ? 

8.  Mary  spends  15^  at  a  fair,  which  is  10  %  of 
what  she  had.     How  much  did  she  have  ? 

9.  In  a  battle  an  army  lost  1815  men,  which 
was  3  %  of  the  number  of  men  engaged.  How 
many  men  took  part  in  the  battle  ? 


PERCENTAGE  211 

10.  An  orchardist  has  75  orange  trees,  which  is 
60  %  of  his  number  of  lemon  trees.  How  many 
lemon  trees  has  he  ? 

11.  A  merchant  saves  $875  a  year,  which  is 
35  %  of  his  earnings.     Find  his  earnings. 

12.  An  agent  collected  money  for  me,  and  I  paid 
him  $  14.40  for  his  services.  This  was  6  %  of 
what  he  collected.     How  much  did  he  collect  ? 

Oral  Problems 

253.  1.  Albert  has  48^  and  spends  25  %  of  it 
for  writing  paper  and  50  %  of  it  for  firecrackers. 
How  much  does  he  spend  on  writing  paper? 
How  much  on  firecrackers  ? 

2.  William  has  96^  and  spends  50  %  of  it  for 
entertainment.  How  many  cents  has  he  left  ? 
Had  he  spent  only  25  %,  how  much  would  be  left  ? 

3.  A  farmer  bought  a  house  for  $  200  and  sold 
it  at  a  loss  of  7^  % .     What  did  he  receive  for  it  ? 

4.  A  ranchman  bought  400  sheep  from  one 
man,  and  75  %"  as  many  sheep  from  another. 
How  many  did  he  buy  all  together  ? 

5.  A  merchant  buys  suits  at  $  20  each  and 
wants  to  sell  them  so  as  to  make  40  %  on  the  cost. 
How  high  must  he  mark  each  ? 

6.  A  boy  gains  $  5  by  selHng  a  bicycle.  This 
is  a  gain  of  10%  of  the  cost.  What  is  his  per 
cent  of  profit  ? 


212  INTERMEDIATE  BOOK 

7.  A  real  estate  dealer  buys  a  lot  for  $  2000  and 
sells  it  for  $  2100.     What  is  his  per  cent  profit  ? 

8.  If  I  sell  my  watch  at  a  gain  of  $  6,  I  gain 
25  % .  Find  the  cost  and  the  selling  price  of  the 
watch. 

9.  A  boy  buys  a  dozen  stamps  for  25^  and  sells 
them  for  30^.     What  is  his  per  cent  of  profit  ? 

10.  A  girl  had  a  number  of  roses.  She  gave 
away  10  of  them.  This  was  50%  of  the  whole 
number.     How  many  roses  had  she  in  all  ? 

Written  Problems 

254.  1.  In  a  ward  12^  %  of  the  registered  voters 
did  not  vote  at  the  last  election.  There  were  70 
who  did  not  vote.     What  was  the  total  registration  ? 

2.  Of  the  votes  cast,  55%  were  for  one  party 
and  45%  for  the  other.  The  winning  party  had 
56  more  votes.     How  many  voted  ? 

3.  Of  the  5800  registered  voters  in  a  city,  899 
fail  to  vote.     What  per  cent  fail  to  vote  ? 

4.  65  %  of  the  blossoms  on  a  small  apple  tree 
failed  to  develop  into  fruit.  The  tree  bore  77 
apples.     How  many  blossoms  did  it  have  ? 

5.  A  poultry  raiser  set  150  eggs.  12  %  failed 
to  hatch.     How  many  eggs  did  hatch  ? 

6.  A  farmer  raised  921  bu.  of  wheat.  He  sold 
33|^%  of  them  at  $  1.05  a  bushel  and  the  rest  for 
95^.     What  did  he  get  for  the  whole  crop  ? 


PERCENTAGE  213 

7.  If  unseasoned  lumber  is  18%  water,  what 
will  125  T.  of  grain  lumber  weigh  after  it  is 
seasoned  ? 

8.  An  acre  of  land  produces  12,750  lb.  of  sugar 
beets.  If  the  beets  are  12^%  sugar,  how  many 
pounds  of  sugar  were  obtained  from  these  beets  ? 

9.  If  a  beef  weighing  1200  lb.  contains  192  lb. 
of  tallow,  what  per  cent  of  the  whole  weight  is 
tallow? 

10.  On  an  experimental  farm  200  seeds  were 
planted  to  test  them.  Of  these  only  105  sprouted. 
What  per  cent  of  the  seed  was  good  ? 

11.  If  an  ounce  of  flower-seed  costs  30^,  and 
50%  of  the  seed  is  good,  what  is  the  price  per 
ounce  of  the  good  seed  ? 

12.  A  fruit  dealer  buys  a  crate  of  oranges  for 
$2.50  and  sells  them  at  2^  each,  making  a  profit 
of  40  %.  How  many  oranges  are  there  in  the 
crate  ? 


APPLICATION   OF   PERCENTAGE 

Oral  Problems 

255.  1.  Sugar  costing  a  merchant  5^  a  pound 
is  sold  by  him  for  6  ^  a  pound.  How  much  is  his 
profit  on  37  lb.  ?  What  per  cent  of  the  cost  is  his 
profit  ? 

2.  If  a  merchant  buys  sugar  at  4  ^  a  pound  and 
sells  it  at  5^,  what  per  cent  of  the  cost  is  his 
profit? 

3.  If  an  automobile  is  bought  for  $1200  and 
sold  later  at  a  loss  of  5  %,  what  is  the  selling  price? 

4.  A  dealer  in  stationery  buys  pencils  at  40  ^  a 
dozen  and  sells  them  at  5  j^  apiece.  What  is  his 
per  cent  of  profit  ? 

Notice  that  the  per  cent  of  gain  or  loss  is  always 
figured  on  the  cost  of  the  goods  or  on  the  sum 
invested. 

5.  A  grocer  buys  grapefruit  at  7  ^  each  and  sells 
them  at  10  ^  each.  What  per  cent  of  profit  does 
he  make  ? 

6.  He  buys  lemons  at  25  ^  a  dozen  and  sells  them 
at  35  ^.     What  per  cent  is  his  profit  ? 

Exercises  and  problems  of  this  character  are 
sometimes  classified  under  the  heading  Gain  or  Loss. 

214 


APPLICATION  OF  PERCENTAGE  215 

Written  Problems 

256.  1.  A  city  lot  was  bought  for  $600,  and 
sold  at  a  loss  of  15  %.  What  was  the  loss  ?  What 
was  the  selling  price  ? 

2.  A  dealer  paid  $  450  for  a  pair  of  horses  and 
sold  them  at  a  profit  of  25  %.  Find  the  selling 
price. 

3.  A  merchant  sold  a  piano  and  gained  $  50.  If 
it  cost  him  $  400,  what  was  his  per  cent  of  gain  ? 

4.  A  merchant  has  $  15,000  invested  in  a  store. 
His  profit  this  year  is  $3000.  What  is  his  per 
cent  of  profit  ? 

5.  What  is  the  per  cent  of  profit,  when  you  buy 
at  $  600  and  sell  at  $  700  ? 

6.  If  I  buy  table  water  at  $  1.10  a  dozen  bottles 
and  sell  it  at  2  bottles  for  25  ^,  what  is  my  per  cent 
of  profit  ? 

7.  If  I  buy  pickles  at  $25.92  for  a  gross  of 
bottles,  and  sell  at  25^  a  bottle,  what  is  my  per 
cent  of  profit  ? 

8.  Clothes  that  cost  $2000  were  damaged  by 
fire  and  sold  at  a  loss  of  17  %.  How  much  was 
lost  ? 

9.  What  is  the  gain  on  bank  stock  bought  at  88 
and  sold  at  96  ? 


216  INTERMEDIATE  BOOK 

Written  Exercise 

257.  Find  the  selling  price,  the  per  cent  gain  or 
loss,  or  the  cost: 

1.  The  cost  is  $  40,  the  loss  is  5  %. 

2.  Loss  7  %,  cost  $  1000. 

3.  The  cost  is  $16,  the  gain  25  %. 

4.  Gain  121%,  cost  $250. 

5.  The  selling  price  $  80,  the  cost  $  75. 

6.  The  selling  price  $  120,  the  cost  $  100. 

7.  The  selling  price  $  225,  the  cost  $  180. 

8.  The  selling  price  $  240,  the  cost  $  250. 

9.  The  selling  price  $  850,  cost  $  100. 

10.    The  selling  price  $  1275,  the  cost  $  1500. 
Make  problems  to  illustrate  these  relations. 

Discount 

258.  Merchants,  manufacturers,  and  business 
houses  frequently  make  a  reduction  or  a  discount 
from  the  catalogue  price  or  the  list  price  to  those 
who  buy  goods  in  large  quantities  and  to  those  who 
pay  cash  for  their  goods.  Discounts  are  often 
offered  by  merchants  in  order  to  increase  trade. 

1.  A  merchant  offered  a  reduction  of  5  %  on 
purchases  amounting  to  $25  or  more.  One  cus- 
tomer bought  $  30  worth  of  goods.  What  reduc- 
tion was  made  ? 


APPLICATION  OF  PERCENTAGE  217 

Any  reduction  made  from  a  fixed  price  is  called 
a  discount.  Discounts  are  usually  reckoned  as  so 
many  per  cent  of  the  fixed  or  list  price.  The  price 
after  the  discount  is  taken  off  is  often  called  the 
net  price. 

2.  A  suit  of  clothes,  marked  at  $35,  is  offered 
at  10  %  off.  How  much  is  the  discount  and  how 
much  is  the  selling  price? 

3.  Goods  damaged  by  fire  were  sold  at  the 
following  discounts : 

Marked  price  :$  15   $39  $60  $120    $24    $77 

Discount:         20  %  10  %   5%     1%    121%   50% 

Find  the  reduced  prices. 

Discount  is  simply  an  application  of  percentage. 
It  involves  no  new  principles. 

The  marked  price  or  list  price  corresponds  to  the 
base. 

The  rate  of  discount  is  the  rate  per  cent. 

The  discount  expressed  as  a  sum  is  the  per- 
centage. 

Oral  Exercise 

259.  Find  the  discount  and  the  reduced  selling 
price  when  the  fixed  or  list  price  and  the  rate  of 
discount  are : 

1.   30^    10%       2.  $44    25%       3.  75^    50% 

4.  40^    15%       5.  $40    75%       6.  48^    25% 
7.   56^    121%     8.  $50      6%       9.  $1       2% 


218  INTERMEDIATE  BOOK 

Written  Problems 

260.  1.  What  is  the  net  price  on  a  set  of  books, 
listed  at  $  25,  when  a  discount  of  20  %  is  allowed  ? 
When  a  discount  of  5  %  is  allowed  ? 

2.  A  shipment  of  bananas  was  slightly  damaged 
in  transit.  It  had  been  valued  at  $  120,  but  the 
buyer  agreed  to  take  it  at  a  discount  of  25  %. 
How  much  was  the  discount  in  dollars?  How 
much  the  selling  price  ?  What  loss  did  the  shipper 
sustain,  if  the  bananas  cost  him  $  95? 

3.  A  lawn  mower,  listed  at  $  5.40,  is  sold  at 
10  %  off.     Find  the  selling  price. 

4.  The  marked  price  on  a  piano  being  $  500  and 
the  rate  of  discount  20  %,  how  much  is  the  discount 
in  dollars  ?  If  you  were  given  the  rate  of  discount 
and  the  amount  of  the  discount,  how  would  you 
find  the  list  price  ?  If  you  were  given  the  list 
price  and  the  discount,  how  would  you  compute 
the  rate  of  discount? 

5.  An  automobile  is  listed  at  $1750.  From 
this  price  there  is  a  discount  of  10  %  and  still  an- 
other discount  of  6%.  What  is  the  net  price  of 
the  automobile? 

Written  Problems 

261.  1.  If  a  set  of  books,  listed  at  $  36,  sells  for 
$  27,  find  the  rate  of  discount. 


APPLICATION  OF  PERCENTAGE  219 

Find  the  first  discount  and  price.  Then  find  the 
second  or  net  price. 

Process 
$S6  —  $27  =  $9      Explanation.  —  The   discount    is 
'25  $36-127  =  89. 

36)9.00  9  -r-  36  =  ^  =  25  %,  the  rate  of  dis- 

rj2  count. 

JgO"  Solve  by  fractions  when  possible. 

180  Thus:  9-36  =  /^=i=25%. 

2.  Find  the  net  price  on  goods  listed  at  $  3360, 
when  a  discount  of  SS^%  is  allowed. 

3.  A  merchant  offers  cloth  at  $  1.50  a  yard,  sub- 
ject to  a  discount  of  16|%.  What  is  the  net  price 
a  yard?  How  man}'^  yards  can  be  bought  for  $45? 
What  part  of  $lare  16f^? 

4.  Find  the  net  price  of  a  table  listed  at  $36, 
discount  16f  %. 

5.  A  store  sells  desks  at  30  %  off.  What  is  the 
selling  price  of  one  marked  $25.75? 

6.  A  hardware  merchant  gives  an  order  for 
350  lb.  of  nails  at  24^  a  pound,  discount  35%. 
How  much  was  his  bill?    • 

7.  A  man  buys  50  ft.  of  garden  hose  at  9|)^  a 
foot,  discount  15  %.     How  much  does  he  pay? 

8.  A  merchant  advertises  25  %  discount  on  cash 
purchases.  A  lawn  mower,  listed  at  $  7.65,  can  be 
bought  for  what  sum? 


220 


INTERMEDIATE  BOOK 


9.    An  article,  marked  $2.50,  sells  for  $2.25. 
What  is  the  rate  of  discount? 

10.    If  an  article,  listed  at  $  3.80,  sells  at  $  3.42, 
find  the  rate  of  discount. 

262.   Find  the  numbers  that  belong  in  the  blank 
spaces : 


List  Prick 

Ratb  of 
Discount 

Net  Price 

List  Price 

Rate  of 
Discount 

Net  Price 

1.  $4.50 

16f% 

11. 

$  525.75 

1  515.23 

2.      3300 

33r/o 

12. 

278.40 

4% 

3.      4760 

12|% 

13. 

979.97 

5% 

4.       860 

$731 

14. 

275.50 

259.07 

5.       950 

16% 

15. 

478.88 

431.00 

6.      200 

150 

16. 

9648.72 

8% 

7.       540 

351 

17. 

4887.75 

10% 

8.       1750 

4% 

18. 

8425.25 

16|% 

9.       1800 

90 

19. 

9637.75 

7510.20 

10.      2175 

5% 

20. 

7475.40 

25% 

Commission 

263.  When  a  person  is  engaged  as  an  agent  to 
transact  business  for  another,  he  usually  is  paid  a 
certain  per  cent  for  his  services.  The  amount  thus 
paid  is  called  commission. 

1.  An  agent  sells  a  lot  for  me  at  $  800  and  I  pay 
him  5  %  of  this  sum  for  his  services.  How  much 
was  his  commission? 

2.  John  Smith  sells  for  John  Brown  10  A.  of 
land  at  $  50  an  acre  at  a  commission  of  3  % .     How 


APPLICATION  OF  PERCENTAGE  221 

much  was  Smith's  commission?  After  taking  out 
his  commission,  how  much  more  does  he  turn  over 
to  Brown? 

Commission  is  one  of  the  applications  of  per- 
centage. The  sum  collected,  the  value  of  the 
goods  or  property  bought  or  sold,  the  sum  men- 
tioned in  the  contract,  corresponds  to  the  base. 

The  rate  of  commission  is  the  rate  per  cent. 

The  commission  expressed  as  a  sum  is  the  per- 
centage. 

Oral  Problems 

264.  1.  If  an  agent  charges  8  %  of  one  month's 
rent  for  his  services,  what  is  his  commission  for 
finding  tenants  for  a  house  that  rents  for  $60  a 
month?     For  a  house  that  rents  for  $  75  a  month? 

2.  A  lawyer  collects  a  debt  of  $  500  and  receives 
10%  of  it  for  his  services.  How  much  does  he 
send  his  employer  after  deducting  his  commission? 

3.  The  contract  for  building  a  house  is  $  6000. 
The  architect  is  allowed  5  %  for  supervising  the 
construction.     What  is  his  commission? 

4.  An  agent  sells  books  on  commission.  He 
sells  a  $40  set  and  receives  a  commission  of  25%. 
What  is  his  commission  ? 

5.  A  doctor  gave  his  accounts  to  a  collector.  If 
the  collector  receives  20  %  for  collections,  what  will 
he  receive  on  a  $25  account? 


222  INTERMEDIATE  BOOK 

Written  Problems 

265.  1.  I  bought  through  an  agent  10  bags  of 
coffee,  each  containing  120  lb.,  at  15^  a  pound. 
The  agent  charged  4  %  commission.  How  much 
did  I  pay  the  agent?  How  much  did  the  coffee 
cost  me,  including  the  commission? 

2.  Acting  as  an  agent,  I  buy  for  W.  Burgess  & 
Co.,  75  barrels  of  flour  at  $  4.50  a  barrel.  I  charge 
a  commission  of  3  % .  How  much  commission  do  I 
receive? 

3.  A  real  estate  agent  receives  for  his  services 
5%  of  the  rents  collected  on  three  houses,  one 
renting  for  $  40  a  month,  another  for  $  75  a  month, 
and  the  third  for  $87  a  month.  How  much  does 
he  receive  a  year  for  his  services? 

4.  A  merchant  gave  bills,  aggregating  $  360,  to 
an  agent  for  collection.  The  latter  succeeded  in 
collecting  only  $240  and  reported  the  remainder 
uncollectible.  How  much  does  the  merchant  lose 
if  he  pays  the  agent  10%  on  the  amount  collected  ? 
What  per  cent  of  the  $  360  did  the  merchant 
lose? 

5.  An  agent  for  farm  machinery  sells  to  a* 
farmer  a  mowing  machine  for  $250.  After  de- 
ducting his  commission  of  12|-%  he  sends  the 
balance  to  the  manufacturers.  How  much  does  he 
send  ? 


APPLICATION  OF  PERCENTAGE 


223 


6.  An  auctioneer  received  $23.40  for  selling 
$  588  worth  of  goods.  What  was  his  rate  of  com- 
mission ? 

7.  I,  as  agent,  sold  a  carload  of  fruit  for  $  476. 
If  I  retained  7  %  for  my  services,  how  large  a  sum 
did  I  transmit  to  my  employers? 

8.  A  commission  merchant  sold  60  boxes  of 
oranges  at  $  2  a  box.  Find  his  commission  at  5  % 
and  the  amount  sent  to  his  employer. 

9.  An  agent  collects  house  rent  for 
the  owner  of  the  house  and  charges 
5  %  of  the  rent  of  his  services.  If  the 
rent  is  $50  a  month,  how  much  does 
the  agent  get  a  year? 

10.  Find  the  commission  on  the  sale 
of  $  700  worth  of  goods  at  the  rate  of 
7  %  on  the  selling  price. 


Drill  Exercise 

266.  Use  drill  device  for  Percentage, 
Commission,  and  Discount.  Change 
the  rate.  Use  5,  10,  50,  75,  etc. 
Change  the  numbers. 


500 


400 


300 


200 


100 


550 


450 


150 


160 


175 


80 


75 


50 


X  .20 


INTEREST 

Introduction 

267.  If  I  borrow  money  from  John  Smith,  not 
only  must  I  return  the  money  to  him  after  a  cer- 
tain period  of  time  mutually  agreed  upon  but  I 
must  pay  him  for  the  use  of  his  money.  This 
extra  sum  that  I  pay  him  is  called  interest. 

Interest  is  the  money  paid  for  the  use  of 
money. 

The  sum  borrowed  is  called  the  principal. 

The  principal  and  the  interest,  added  together, 
give  the  amount. 

When  we  say  that  the  rate  of  interest  is  4  % 
or  6  %,  we  mean  that  the  rate  per  annum  (by  the 
year)  is  4  %  or  6  % . 

1.  What  is  the  interest  on  $300  for  1  yr.  at 

6  %  ?   at  3  %  ? 

2.  What  is  the  interest  on  $500  for  1  yr.  at 

5  %  ?  at  4  %  ? 

3.  What  is  the  interest  on  $  600  for  6  mo. 
at  5  %  ?  In  finding  the  interest  for  6  mo.  you 
first  find  the  interest  for  1  yr.  and  then  divide 
by  12. 

224 


INTEREST  225 

Oral  Exercise 

268.  Find  the  interest  for  1  mo. : 

1.    $  500  at  7  %  2.    $  60  at  6  % 

3.    $1000  at  6%  4.    $7000  at  4% 

5.    $  700  at  8  %  6.    $  70  at  4  % 

7.    $800  at  5%  8.    $900  at  7% 

Find  the  interest  on  each  of  these  sums  for  6  mo. 

Tell  how  to  find  the  interest  on  $  100  for  6  mo. 
at  6%. 

Tell  how  to  find  the  interest  on  a  sum  of  money 
for  3  mo. 

Oral  Exercise 

269.  Find  the  interest  for  6  mo. ;  for  3  mo. : 
1.    $200  at  6%                    2.  $800  at  5% 
3.    $  300  at  8  %                    4.  $  900  at  4  % 
5.    $500  at  5%                    6.  $1000  at  6% 
7.    $  700  at  8  %                    8.  $  800  at  9  % 
9.    $400  at  7%                  10.  $2000  at  3% 

Tell  how  to  find  the  interest  on  a  sum  of 
money  for  3  mo. ;  for  1  mo. ;  for  any  number  of 
months. 

Written  Exercise 

270.  1.  Find  the  interest  on  $350  at  6%  for 
6  mo. ;  for  4  mo. ;  for  3  mo. 

Q 


226  INTERMEDIATE  BOOK 

Process 
7        ^ 

2 

Explanation.  —  Multiply  the  sum  at  interest  by 
the  rate  of  interest  expressed  as  a  decimal  fraction  and 
by  the  number  of  months  expressed  as  part  of  a  year. 
Use  cancelation  when  possible. 

2.  What  is  the  interest  on  $475  at  5%  for 
6  mo.  ?  for  3  mo.  ?  for  4  mo.  ? 

3.  Reckon  the  interest  on  $465.50  for  2  yr.  at 
6%. 

4.  Compute  the  interest  on  $505.50  for  3  yr. 
at  5  % . 

5.  Find    the   interest   on    $  675.25    for    5   yr. 

at  3%. 

6.  Find  the  interest  on  $  325.40  at  4  %  for  1  yr. 
and  6  mo. 

7.  By  how  much  does  the  yearly  interest  on 
$  375  at  5%  exceed  the  yearly  interest  on  $400  at 
4%? 

8.  How  much  are  the  principal  and  interest 
together  on  $575  at  5%  at  the  end  of  one  year? 
What  is  the  amount  ? 

9.  Find  the  amount  at  the  end  of  two  years  of 
$565.50  at  4%. 

10.    Find  the  amount  of  $  1000  for  3  yr.  at  6  %. 


INTEREST  227 

Oral  Exercise 

271.  1.    What  is  the  interest  on  $  120  at  5  %  for 
1  yr.  ?   1  mo.  ? 

2.  Find  the  uiterest  on  $  240  at  10  %  for  1  yr. 
1  mo. 

3.  Compute  the  interest  on  $  200  at  6  %  for 

1  yr. ;  for  1  mo. 

4.  How  much  interest  must  you  pay  on  $  300 
at  8  %  for  1  yr.  1  mo.  ? 

5.  What  is  the  interest  on  $300  at  6%  for 

2  mo.  ?     2  mo.  are  what  part  of  12  mo.  ? 

6.  What  is  the  amount  of    $200   at  6%  for 

I  yr.  and  1  mo.  ? 

7.  Find  the  amount  of  $  600  at  4  %  for  1  yr. 
and  1  mo. 

8.  Find  the  interest  on  $  120  at  5  %  for  1  mo. ; 
for  7  mo.;  for  11  mo. 

9.  What  is  the  interest  on  $  240  at  10  %  for 

II  mo.  ? 

10.   What  is  the  interest  on  $  500  for  2  yr.  8  mo. 

at  3  %  ? 

Written  Exercise 

272.  Find  the  interest : 

Pkin.         Rate        Time  Prin.  Rate         Time 

1.    $300,    6%,  2  mo.         2.    $200,    3%,  2  mo. 
3.    $  100,    5  %,  3  mo.        4.    $  50,      6  %,  4  mo. 


228 


INTERMEDIATE  BOOK 


Pbin. 


Eate         Time 


Pein. 


Kate        Time 


5.    $150,    6%,  6  mo.        6.    $500,    6%,  4  mo. 

7.    $600,    4%,  5  mo.        8.    $400,    4%,  3  mo. 

9.  $430,  5%,  6  mo.  lo.  $650,  6%,  9  mo. 
11.  $  1000,  4  %,  8  mo.  12.  $  1560,  5  %,  8  mo. 
13.  $2575,  6%,  10  mo.  i4.  $8975,  7%,  7  mo. 
15.    $6875,  8%,  8  mo. 


Study  Exercise 
273.   Find  the  interest  and  the  amount : 
1.    $  525.75  for  2  yr.  and  5  mo.  at  3  % . 
Process 
Int.  for  1  yr.        Int  for  2  yr, 


$525.75 
X.03 
$15.77 
Int.  for  1  mo. 

$1.31 
12)$  15.77 


$15.77 

X.02 

$31.54 

Int.  for  5  mo. 

$1.31 

X.5 

$6.55 


$31.54  Int.  for  2yr. 

6.55  Int.  for  5  mo. 
$38.09  Int.  for  2  yr.  5  mo. 
$  525.75  Principal 

38.09  Interest 
$563.84  Amount 


Explanation.  — 
Find  the  interest  on 
the  sum  at  the  re- 
quired rate  for  one 
year.  Find  the  in- 
terest for  the  num- 
ber of  years.  Find 
the  interest  for  one 
month,  -^^  the  in- 
terest for  1  year. 
Find  the  interest 
for  the  number 
of  months.  Add 
the  interest  for 
the  years  and  the 
months.  Add  the 
principal  to  the  in- 
terest to  get  the 
amount. 


INTEREST 


229 


Written  Exercise 

274.  Find  the  interest  and  the  amount  : 

1.  $307.25  at  6%  for  5  yr. 

2.  $906  at  5%  for  1^  yr. 

3.  $175.40  at  4%  for  li  yr. 

4.  $  263  at  7  %  for  1  yr.  3  mo. 

5.  $  650  at  5  %  for  1  yr.  1  mo. 

6.  $  780  at  4  %  for  2  yr.  9  mo. 

7.  $  690  at  7  %  for  3  yr.  8  mo. 

8.  $  360  at  5  %  for  4  yr.  7  mo. 

9.  $  1200  at  9  %  for  5  yr.  5  mo. 
10.    $  94.60  at  6  %  for  1  yr.  6  mo. 

Written  Exercise 

275.  Find  the  interest  and  the  amount : 
1.    $  785.45  for  1  yr.  2  mo.  at  41%. 


$785.45 
.045 
392725 
314180 


Process 

$5.89  (2  mo.) 
6)35:35 
$35.34 
5.89 


Explanation 
41%  =  .045 
2  mo.  =  Joflyr. 
Use  135.35  as 
$  35.34525  (1  yr.)        $  41.23  Ans.    interest  for  1  yr. 

2.  $375.35  for  3  yr.  4  mo.  at  5i%. 

3.  $  750.45  for  2  yr.  6  mo.  at  4|%. 

4.  $  4850.75  for  5  yr.  4  mo.  at  5^%. 


230  INTERMEDIATE  BOOK 

5.  $  7525.25  for  1  yr.  8  mo.  at  2|  %! 

6.  $  8759.40  for  4  yr.  9  mo.  at  2|%  . 

7.  $2002.60  for  1  yr.  10  mo.  at  4f  %. 

8.  $5000  for  1  yr.  1  mo.  at  61%. 

Written  Problems 

276.  1.  I  borrow  $375  at  7%  for  1  yr.  and  3 
mo.  How  much  must  I  pay  back  at  the  end  of 
that  time? 

2.  I  borrow  $2000  at  6%  for  2  yr.  With  this 
money  I  buy  a  small  lot  and  build  upon  it  a  cottage. 
At  the  end  of  two  years,  I  sell  the  cottage  and  lot 
for  $2500.  Do  I  gain  or  lose  by  this  transaction? 
How  much? 

3.  A  real  estate  agent  buys  a  house  for  $  1500. 
He  must  pay  $  50  every  year  for  taxes,  insurance, 
and  repairs.  For  how  much  per  month  must  he 
rent  the  house  to  make  6  %  on  the  cost  of  the 
house? 

4.  I  borrow  $  60  from  Mr.  Brown  for  9  months 
at  6%.     How  much  interest  must  I  pay  him? 

5.  Mr.  James  borrows  $75  from  a  friend  and 
promises  to  pay  it  back  in  4  months  at  6  % .  How 
much  is  the  interest  for  that  time?  Find  the 
amount  that  Mr.  James  must  pay  at  the  end  of  the 
4  months. 


INTEREST  231 

Interest  Accounts 

277.  Any  person  ten  years  of  age  or  over  may 
deposit  money  at  interest  at  the  post  office,  with 
the  security  of  the  United  States  government  for 
repayment.  Money  may  also  be  deposited  in 
banks,  savings  banks,  and  trust  companies  where 
it  will  draw  interest  according  to  the  rules  of  the 
institution. 

In  postal  savings  banks,  interest  is  allowed  at 
the  rate  of  2  %  for  each  full  year  that  the  money 
remains  on  deposit.  The  interest  is  computed  from 
the  first  day  of  the  month  following  the  day  on 
which  the  money  is  deposited. 

In  savings  banks  and  trust  companies  the  in- 
terest rate  varies.  It  is  usually  3  %  or  3 J  %.  The 
interest  is  usually  computed  from  the  first  day  of 
the  month  following  the  day  on  which  the  money 
is  deposited.  In  these  institutions  interest  is 
usually  paid  quarterly  or  semiannually. 

Written  Exercise 

278.  Compute  the  interest  on  deposits  in  postal 
savings  banks  as  follows : 

1.  $  50,  deposited  May  6,  1914,  withdrawn  June 
5,  1915. 

2.  $70,  deposited  Jan.  4,  1914,  withdrawn  Dec. 
17,  1914. 


232  INTERMEDIATE  BOOK 

3.  $95,  deposited  April  29,  1915,  withdrawn 
May  1,  1917. 

4.  $  75,  deposited  June  15,  1914,  withdrawn 
June  1,  1916. 

5.  $  64,  deposited  Sept.  3,  1913,  withdrawn 
Oct.  1,  1915. 

Written  Exercises 

279.  1.  Find  out  how  often  interest  is  paid  on 
accounts  in  the  local  savings  bank. 

2.  What  rate  of  interest  is  paid  by  the  local  bank 
on  savings  accounts  ? 

3.  Find  out  how  interest  is  computed  on  savings 
bank  accounts. 

4.  Make  an  account  of  savings  deposited  in  a 
savings  bank.  Can  you  compute  the  interest  on 
the  account  at  the  end  of  one  year  ? 

5.  How  is  interest  computed  using  the  interest 
table  ? 


BILLS   AND    CHECKS 


Introductory 

280-  1.  Mrs.  James  Downs  makes  several  pur- 
chases at  the  store  of  Milton  Bros.  &  Co.  The 
articles  are  shown  in  the  following  bill : 

San  Francisco,  Sept.  15. 
Mrs.  James  Downs, 

Bought  of  MILTON   BROS.  &  CO., 

165  Market  St.  Phone  204 


2^  lb.  steak 
1  lb.  tea 
4  lb.  butter 
10  lb.  beet  sugar 


28  j^ 
45  j^ 
35^ 


70 
45 
40 
50 


05 


What  are  the  articles  purchased  ? 

What  is  the  price  of  each  article  ? 

How  much  is  the  entire  bill  ? 

Where  and  when  were  the  articles  sold  ? 

Who  is  the  buyer  ?     The  seller  ? 

After  the  bill  was  paid  by  Mrs.  Downs,  the  clerk 
wrote  the  w^ords  "  Received  payment,  Milton  Bros. 
&  Co.  per  J.  F."  The  words  show  that  the  bill  is 
paid.     The  bill  is  now  called  a  "  receipted  bill." 

"  J.  F."  are  the  initials  of  the  clerk's  name. 

233 


234 


INTERMEDIATE  BOOK 


The  receipted  bill  should  be  kept  by  the  buyer 
to  show  that  the  bill  has  been  paid. 

2.  Mr.  J.  W.  Jones  goes  to  the  bookstore  of 
Burgess  &  Co.  and  buys  books  and  stationery. 
He  receives  a  bill  and  pays  it.  What  does  the 
clerk  in  the  store  write  on  the  bill  to  show  that  it 
has  been  paid  ? 

The  receipted  bill  is  as  follows : 

Madison,  Wis.,  Dec.  1. 
Mr.  J,  W.  Jones, 

Bought  of  BURGESS  &  CO., 

105  State  St.  Phone  714 


Nov. 


12 


1  arithmetic 
1  geography 
3  lead  pencils 


Received  payment 
Burgess  &  Co. 

per  B.  C. 


45 

85 
15 


45 


3,    Mrs.  A.  Smith  orders  from  Gerry  &  Co. : 

4  lb.  coffee  at  30^  a  pound 
18  lb.  sugar  at  5^^  a  pound 

5  gal.  molasses  at  60.^  a  gallon 

Make  out  the  bill  which  Gerry  &  Co.  send  Mrs. 
Smith.  How  much  does  Mrs.  Smith  owe  ?  Indi- 
cate what  must  be  written  on  the  bill  to  show  that 
it  has  been  paid. 


BILLS  AND  CHECKS  235 

4.  Make  out  bills  of  the  following  items,  using 
your  father's  name  as  buyer  and  the  name  of  your 
local  merchant  as  seller : 


2  bags  salt       @  $  .10 

15  yd.  silk       @ 

$1.50 

3  bu.  potatoes  @     .75 

12  yd.  muslin  @ 

.09 

10  lb.  prunes     @     .121 

9  yd.  lace       @ 

.65 

5.  Make  out  4  bills  for  goods  purchased  of  the 
local  dealers. 

6.  If  a  person  has  money  deposited  in  a  bank, 
he  may  pay  a  bill  by  check,  thereby  ordering  the 
bank  to  pay  the  sum  specified. 


Form  of  a  Check 

JVo,  89 

ISanJt  of  aEtsconsin 

Madison,  Wis.,  fwUf 

/^. 

1^/6. 

Pay  to  the  order  of famv&o.  W^oa^.- 



..f  36.^6 

^klvtl^   jiA}-& 

a.'yvcL  //^-r^rvr-i^or-r^^^rrrc^r-^- 

>c^ 

^.Dollars 

^o-yva 

u 

^v&c^. 

Name  the  sum  paid.     Who  ordered  it  paid  ? 

To  whom  is  the  amount  paid  ? 

In  what  bank  does  Donald  Gregg  have  his 
money  deposited  ? 

How  much  does  this  check  reduce  the  amount 
of  Donald  Gregg's  deposit  in  the  bank  ? 

When  James  Ward  presents  the  above  check  at 


236  INTERMEDIATE  BOOK 

the  bank,  he  writes  his  name  on  the  back  of  the 
check  and  either  receives  the  $  35.45  from  the 
bank  in  cash  or  has  it  added  to  his  own  deposit  in 
the  bank.  The  writing  of  his  name  across  the 
back  is  called  indorsing  the  check  and  is  evidence 
that  the  sum  has  been  received  by  him.  The  bank 
returns  the  indorsed  check  to  Donald  Gregg,  who 
keeps  it  as  evidence  that  the  sum  has  been  paid. 

7.  John  Ward  has  his  money  deposited  in  the 
First  National  Bank  of  Lawrence,  Kansas.  He 
wished  to  pay  Richard  March  of  that  city  the  sum 
of  $  105.25.     Write  the  check. 

8.  Write  out  checks  of  your  own  on  the  sup- 
position that  you  had  money  deposited  in  the 
Second  National  Bank  of  Liliputia. 


PROBLEMS    ON   INDUSTRY 
281.   Table  for  Reference  in  Agricultural  Problems 


Kind  of  Cboh 

AvEBAGB  Amount 
OF  Febtilizees 

PEK  ACKE 

Average  Amount 
OF  Seed 
PER  Acre 

Average  No.  of 
Weeks  to 

Maturity 

Corn 

10  T. 

10  qt. 

15i 

Fall  wheat 

18  T. 

2bu. 

42 

Oats 

7iT. 

5ipk. 

13 

Potatoes 

171  T. 

14  bu. 

16 

Turnips 

10  T. 

2  1b. 

10 

Problems  Based  on  the  Table 

282.  1.  How  much  more  fertilizing  material  is 
used  per  acre  for  fall  wheat  than  for  corn  ?  What 
per  cent  of  10  T.  is  this  excess  ?  Comparing  pota- 
toes and  com,  what  per  cent  of  10  T.  is  the  excess  ? 

How  much  less  fertilizing  material  per  acre 


2. 

is  used  for  oats  than  corn  ? 
10  T.  is  this  difference  ? 


What  per  cent  of 


3.  What  per  cent  of  the  fertilizers  used  for  corn 
is  that  used  for  wheat  ? 

4.  How  much  fertilizing  material  is  needed  for 
SOJ  A.  of  potatoes  ?     7  A.  of  oats  ? 

5.  How  many  acres  of  land  for  wheat  can  be 
fertilized  from  50  loads  of  material,  f  T.  per  load  ? 

237 


238  INTERMEDIATE  BOOK 

6.  How  many  quarts  more  of  wheat  than  of 
corn  are  needed  on  8  A.  ? 

7.  How  many  pecks  less  of  oats  than  of  wheat 
are  seeded  on  10  A.  ? 

8.  How  many  more  acres  can  be  seeded  with 
154  bu.  of  potatoes  than  with  20  lb.  of  turnips  ? 

Written  Problems 

283.  Refer  to  the  table  on  page  237  for  facts 
necessary  to  the  solution  of  the  problem. 

1.  When  may  we  expect  corn  planted  on 
May  15th  to  mature? 

Process 
Mav  16  da  Explanation.  —  Count  off  the  weeks 

J         orj  -j   *      on  a  calendar,  or  proceed  thus  :  15^  wk. 

T  ^Ql^^*      =^^^^   ^^•'     ^"^    ^^P*-    ^    ^""^    ^^^    ^^• 
July  31  da.     Therefore  the  required  date  is  Sept.  1 

Aug.  31  da.     or  2. 
108  da. 

2.  How  many  more  acres  can  be  seeded  with 
493  bu.  of  potatoes  than  with  63  bu.  of  turnips  ? 

3.  About  what  date  may  we  expect  wheat 
seeded  Sept.   25th  to  mature? 

4.  How  many  bushels  and  pecks  less  of  oats 
are  seeded  on  74^  A.  than  of  wheat  over  an  equal 
area  ? 

5.  How  much  fertilizing  material  is  needed  for 
210J  A.  of  potatoes  and  2T|-  A.  of  oats  ? 


PROBLEMS  ON  INDUSTRY  239 

6.  What  per  cent  of  the  fertihzer  per  acre  on  a 
wheat  field  are  the  fertilizers  commonly  put  on  a 
1-acre  potato  patch  ? 

7.  What  per  cent  of  the  fertilizers  for  4  A.  of 
oats  are  the  fertilizers  needed  for  2  A.  of  wheat  ? 

8.  Mr.  Jones  agrees  to  cover  12|-  A.  of  corn 
land  with  fertilizers  at  $  .75  a  load,  and  to  allow 
5%  discount  for  payment  within  10  days.  How 
much  will  he  be  paid,  if  he  allows  the  discount  ? 

9.  A  ranchman  buys  potatoes  at  $  .60  a  bushel 
for  planting  50^  acres  and  is  allowed  a  discount  of 
7  %.     How  much  does  he  pay  ? 

10.  In  seeding  tobacco,  1  oz.  of  seed  is  applied 
to  6  sq.  rd.  How  many  ounces  is  this  for  1 
sq.  rd. ?     For  160  sq.  rd.  or  1  A.? 

11.  What  fraction  of  an  ounce  of  seed  is  that  for 
Isq.  yd.? 

12.  In  case  of  tomatoes,  6^  oz.  of  seed  usually 
suffice  per  acre.  What  part  of  an  ounce  is  needed 
for  1  sq.  rd.? 

13.  Tomatoes  seeded  in  the  Southern  states 
ordinarily  ripen  in  16  weeks,  but  this  year  they 
take  5  days  longer  than  the  usual  time.  On  what 
date  should  they  be  picked  if  they  were  seeded 
Feb.  15  ? 

14.  A  farmer  plans  to  harvest  his  oats  on 
July  25.  What  would  seem  to  be  the  most  favor- 
able time  for  putting  in  the  seed  ? 


240  INTERMEDIATE  BOOK 

15.  In  planting  sweet  potatoes  11^  bu.  are 
usually  needed  per  acre.  How  many  bushels 
must  be  procured  for  17.6  A.,  if  5%  more  than 
the  amount  named  are  to  be  planted  per  acre? 

Written  Problems 

284.  1.  In  the  spring  and  summer  the  salmon 
leave  the  sea  and  proceed  up  the  rivers  to  places 
where  the  river  water  is  cool.  There  they  deposit 
their  eggs  and  then  die.  Young  fish  develop  from 
the  eggs  and  float  downstream  into  the  ocean. 
Salmon  starting  up  the  Columbia  River  early  in 
March  move  at  first  only  about  2^  miles  a  day. 
How  many  rods  a  day  is  this  ?  How  many  yards 
a  day  ?     How  many  feet  a  day  ? 

2.  If  they  travel  13,200  ft.  a  day,  how  far  do 
they  go  in  an  hour  on  an  average  ? 

3.  Later  the  salmon  move  faster,  reaching,  per- 
haps, a  speed  of  6  mi.  a  day.  How  far  can  they 
go  at  that  rate  in  the  month  of  May  ?  What  per 
cent  of  6  mi.  is  the  former  rate  of  2^  mi.  ? 

4.  Some  salmon  go  up  the  Columbia  River 
1000  mi.  to  tributaries  fed  by  melting  snow  in 
Idaho.  If  a  fish  left  the  ocean  March  1,  traveled 
1000  mi.,  and  reached  the  cold  waters  in  Idaho 
on  Oct.  1,  how  many  days  was  it  traveling  ?  How 
many  miles  did  it  average  a  day.  If  it  made 
4.7  mi.  a  day,  how  many  feet  a  day  did  it  travel  ? 


PROBLEMS  ON  INDUSTRY  241 

5.  When  salmon  come  to  a  low  waterfall,  they 
leap  atop  of  it.  A  salmon  jumps  atop  of  one 
12  ft.  high.  How  many  times  higher  is  this  than 
Harry's  running-high-jiimp  record  of  4  ft.  6  in.? 

6.  While  ascending  streams  the  salmon  eat 
nothing  and  consequently  lose  weight.  If  a  salmon 
weighed  20  lb.  at  the  beginning  of  its  trip  and 
16  lb.  at  the  end  of  it,  what  per  cent  of  its  original 
weight  did  it  lose  ? 

7.  Another  salmon  weighed  at  first  30  lb.  and 
then  lost  16  %.     What  was  its  final  weight  ? 

8.  The  young  fish  float  down  the  river,  tail 
foremost.  If  it  takes  them  11  months  to  descend 
1000  miles  to  the  ocean,  how  many  miles  do  they 
make  a  month  ? 

9.  If  a  young  salmon  is  4  in.  long  when  it  first 
reaches  the  ocean,  and  is  2^  ft.  long  when  later  it 
ascends  the  river,  how  many  times  has  it  increased 
its  length  while  in  salt  water  ? 

10.  No  other  fish  is  canned  so  extensively  as  the 
salmon.  The  Columbia  River  yielded  during  the 
6  yr.  ending  1880  about  150,000,000  lb.  of  salmon. 
If  the  fish  averaged  30  lb.,  how  many  fish  were 
killed  ? 

11.  In  one  year  31,500,000  pound  cans  of  salmon 
were  shipped  from  the  Oregon  coast,  valued  at 
$  3,300,000.  Compute  to  cents  and  mills  the 
value  per  can. 


242  INTERMEDIATE  BOOK 

12.  The  value  of  the  entire  salmon  catch  on  onr 
west  coast,  including  Alaska,  exceeds  S  13,000,000 
annually.  If  65%  of  this  is  from  canning  the 
species  known  as  chinook  salmon,  how  many 
dollars  come  from  other  species  of  salmon  ? 

13.  A  firm  desire  to  expend  $  75,000  upon  a 
salmon-canning  factory,  but  have  only  $  36,000  in 
cash.  They  borrow  the  balance  at  3^  %.  How 
much  interest  must  they  pay  annually  ? 

14.  An  agent  sells  50,000  cans  of  salmon  for 
this  firm,  at  $  .09  a  can,  and  charges  2  %  com- 
mission. How  much  money  does  he  send  to  the 
firm  after  deducting  his  commission  ? 

15.  It  is  feared  that  the  salmon  will  be  ex- 
terminated before  many  years.  One  year  Oregon 
yielded  39,500,000  lb.  of  salmon.  If  the  year  fol- 
lowing 10  %  less  was  canned,  how  many  pounds 
were  canned? 

16.  Salmon  are  known  to  have  reached  the 
weight  of  100  lb.  What  per  cent  is  this  of  the 
average  weight  of  25  lb.  ? 

17.  In  Monterey  Bay  salmon  are  caught  by 
trolling,  the  hook  being  baited  with  sardine;  25 
fish  by  one  line  is  a  big  day's  catch.  If  the  fish 
caught  average  19  lb.  and  sell  at  $  .05  a  pound, 
what  is  the  value  of  a  day's  catch  ? 

18.  If  the  speed  in  trolling  is  4  mi.  an  hour,  and 
a  man  trolls  7f  hr.,  how  far  will  he  have  gone  ? 


PROBLEMS  ON  INDUSTRY  243 

19.  If  5  gallons  of  oil  are  used  in  moving  the 
boat  during  7  hours,  oil  costing  $  .16  a  gallon, 
what  is  the  cost  of  oil  for  a  21-hour  cruise  ? 

20.  One  observer  found  the  average  weight  of 
salmon  in  the  Columbia  River  to  be  22  lb.  and  in 
the  Sacramento  River  16  lb.  What  per  cent  was 
the  latter  of  the  former  ? 

21.  In  trolling  in  Monterey  Bay,  fishermen  let 
out  about  150  ft.  of  line.  Through  what  distance 
in  yards  must  the  line  be  drawn  in  while  catching 
24  fish  ? 

Written  Problems 

285.  This  dia- 
gram shows  the 
standard  method  of 
cutting  meat.  Sup- 
pose the  weights 
and  pieces  of  the 
different  kinds  to  be 
as  follows : 


Table 

for  Reference 

Neck,  27  lb.  at  $  .13 

Porterhouse,  95  lb.  at  $  .30 

Chuck,  139  lb.  at  $  .15  Sirloin,  41  lb.  at  $  .25 

Ribs,  74  lb.  at  $  .18 

Flank,  49  lb.  at  $.15 

Shin,  63  lb.  at  $  .06 

Rump,  41  lb.  at  $  .15 

Plate,  120  lb.  at  $.13 

Round,  123  lb.  at  $  .20 

Shank, 

27  lb.  at  $  .06 

244  INTERMEDIATE  BOOK 

Problems  Based  on  the  Table 

286.  1.  Find  the  cost  of  11  lb.  of  each  kind  of 
meat. 

2.  Find  the  cost  of  12  lb.  of  each  kind  of  meat. 

3.  What  is  the  cost  of  lOJ  lb.  of  neck?  of 
round  ?  of  chuck  ? 

4.  What  must  you  pay  for  2 J  lb.  of  ribs  ?  of 
shin  ?  of  flank  ?  If  the  answer  has  ^  cent,  figure 
1  cent  in  place  of  ^. 

5.  What  is  the  cost  of  2  lb.  of  porterhouse 
and  3  lb.  of  plate? 

6.  Find  the  cost  of  5  lb.  of  rump  and  3  lb.  of 
chuck. 

7.  A  purchaser  gets  3  lb.  of  porterhouse  and 
pays  the  bill  with  a  dollar  bill.  How  much  change 
should  he  get  ? 

8.  If  you  order  3  lb.  of  sirloin  and  hand  over 
$  .75,  how  much  change  will  you  receive  ? 

9.  How  much  more  will  30  lb.  of  ribs  cost  than 
35  lb.  of  chuck  ? 

10.  Mr.  Jones  buys  a  piece  of  flank  weighing 
30^  lb.  and  a  piece  of  shin  weighing  20^  lb.  How 
much  does  he  pay  for  both  pieces  ? 

11.  How  much  more  or  less  than  the  piece  in- 
dicated above  does  a  man  pay  for  all  the  porter- 
house and  all  the  sirloin  of  that  one  animal,  if  he 
buys  at  the  rate  of  $  .22  a  pound  ? 


PROBLEMS  ON  INDUSTRY  245 

Written  Problems 

287.  1.  In  1888  the  steamship  PhiladelpJda  was 
built,  560  ft.  long  and  63.3  ft.  broad.  How  many 
times  the  breadth  was  the  length  ?  What  per  cent 
of  the  length  was  the  breadth  ? 

2.  The  Colwnbia,  built  in  1901,  was  503  ft.  long 
and  56  ft.  broad.  Was  this  broader  than  the 
Philadelphia,  in  proportion  to  its  length,  or  less  ? 

3.  If  you  divide  the  length  by  the  breadth,  you 
find  what  is  often  called  the  "  ratio  "  between  the 
length  and  the  breadth.  Find  this  ratio  for  each 
of  the  following  steamers  of  the  Atlantic  Transport 
Line : 

Mesaba,  length  482.1  ft.,  breadth  52.2  ft.,  depth  31.6  ft. 
Minnehaha,  length  600.7  ft.,  breadth  65.5  ft.,  depth  43.3  ft. 
Minnewask,  length  616     ft.,  breadth  66     ft.,  depth  44  ft. 

4.  In  each  case  the  ratio  was  found  to  be  not 

far  from .     It  is  found  that  steamers  built  on 

this  ratio  make  the  best  travelers. 

5.  Find  the  ratio  between  the  length  and  depth 
of  the  steamers  in  Exercise  3.  Is  this  as  fixed  as 
the  other  ratio  ? 

6.  The  Lusitania,  built  in  1906,  was  790  ft.  long, 
88  ft.  broad,  and  60.6  ft.  deep.  How  many  feet 
longer  is  this  than  the  Minnewask^  What  per 
cent  of  the  length  of  the  Minneioask  is  this  excess? 

7.  The  Olympic  is  882  ft.  long.  What  per  cent 
is  this  of  the  length  of  the  Mesaba  f 


246 


INTERMEDIATE  BOOK 


8.  The  Lusitania  has  a  horse  power  of  70,000, 
the  Minnewask  of  1616.  What  is  the  ratio  of  the 
former  to  the  latter  ? 

9.  The  largest  locomotive  for  moving  trains 
has  4000  horse  power.  What  per  cent  is  this  of 
the  Lusitania! s  horse  power  ? 

10.  A  knot  used  in  indicating  distances  on  the 
ocean  is  equal  to  6086  ft.  How  far  is  this  in 
miles  ? 

11.  In  1856  the  Persia  made  the  trip  .between 
New  York  and  Queenstown,  England,  in  9  da. 
15  hr.  45  min.  In  1908  the  Lusitania  made  this 
trip  in  4  da.  15  hr.  Could  the  Lusitania  have 
gone  to  Queenstown  and  back  to  New  York  in  the 
time  it  took  the  Persia  to  go  one  way  ?  What  is 
the  difference  in  time  of  the  two  steamers  for  the 
trip  one  way  ? 


288. 


Written  Problems 
Table  for  Reference 


Rate 

Rate 

Places 

Places 

Day 
Message 

Night 
Message. 

Day 

Message 

Night 
Message 

Alabama 

60-4 

50-3 

Louisiana 

60-4 

50-^ 

California 

1.00-7 

1.00-7 

New  Hampshire 

35-2 

25-1 

Colorado 

75-5 

60-4 

New  York  City 

20-1 

20-1 

Connecticut 

25-2 

25-1 

Tennessee 

50-3 

40-3 

Dist.  of  Columbia 

30-2 

26-1 

Wisconsin 

50-3 

40-3 

Kentucky 

50-3 

40-3 

Yukon,  Dawson 

4.25-29 

4.25-29 

PROBLEMS  ON  INDUSTRY  247 

Explanation.  —  These  rates  are  between  New 
York  City  and  the  places  named.  A  day  rate,  "  60-4," 
means  60  <^  for  10  words  and  4  ^  for  each  additional 
word.  A  night  rate,  50-3,  means  50  (^  for  10  words 
and  3  ^  for  each  additional  word.  Address  and  signa- 
ture are  free. 

A  Night  Letter  is  different  from  a  night  message. 
The  standard  day  rate  for  10  words  is  charged  for 
the  transmission  of  50  words  or  less,  and  \  of  such 
standard  day  rate  for  10  words  is  charged  for  each 
additional  10  words  or  less. 

A  Day  Letter  of  50  words  or  less  is  transmitted 
at  one  and  one-half  times  the  standard  night  letter 
rate. 

Problems 

289.  1.  Find  the  cost  of  sending  a  15-word  day 
message  from  New  York  City  to  Montgomery,  Ala. 
How  much  cheaper  is  a  night  message  ? 

2.  What  is  the  cost  of  a  50-word  night  letter 
from  New  York  City  to  Montgomery?  What  is 
the  cost,  if  sent  as  a  day  letter  ? 

3.  What  is  the  cost  of  a  12-word  message  from 
New  York  City  to  Dawson  ? 

4.  A  man  in  New  York  City  sends  a  20-word 
telegram  to  a  friend  in  a  distant  part  of  that  city. 
How  much  does  he  pay  for  it  ?  Does  he  save  any- 
thing by  sending  it  as  a  night  message  ? 


248  INTERMEDIATE  BOOK 

5.  Find  the  cost  of  wiring  the  following  mes- 
sage from  New  Haven,  Conn.,  to  a  home  in  New 
York  City :  "Yale-Harvard  football  game  a  tie." 

6.  What  is  the  cost  of  a  60-word  night  letter 
sent  from  New  York  City  to  Denver,  Col.  ? 

7.  Find  the  cost  of  sending  a  15-word  telegram 
from  New  York  City  to  New  Orleans,  La.,  at  day 
rates.  How  much  cheaper  is  a  night  message  ? 
What  per  cent  of  the  cost  of  a  day  message  is  this 
saving  ? 

8.  A  25-word  day  message  sent  from  New  York 
City  to  Madison,  Wis.,  costs  how  much  more  than 
a  night  message  ?  What  per  cent  of  the  cost  of 
the  day  message  is  saved  by  sending  a  night 
message  ? 


THE  WESTERN  UNION  TELEGRAPH  COMPANY 

1.45  P.M. 

Chicago,  Feb.  15,  1911. 

To  The  Macmillan  Company, 

64-66  Fifth  Avenue,  New  York  City. 

Send  by  express  ten  copies  Tarr's  New 
Physical  Geography,  twenty  copies  Cole- 
man's The  People's  Health. 

John  Lake. 


9.  If  the  rates  for  Illinois  are  the  same  as  for 
Wisconsin,  what  is  the  cost  of  this  telegram,  night 
rate? 


PROBLEMS  ON  INDUSTRY  249 

10.  Write  telegrams  to  some  of  your  acquaint- 
ances, and  compute  the  cost  of  sending  each. 

11.  What  per  cent  of  the  rate  to  Louisiana  is 
the  rate  to  New  Hampshire  for  10  words?  For 
20  words  ? 

12.  In  1870  the  Western  Union  Telegraph  Co. 
operated  54,000  miles  of  telegraphic  lines  ;  in  1908 
this  had  increased  to  209,000  miles.  What  per 
cent  of  the  miles  in  1870  is  the  increase  in  miles 
shown  in  1908?  On  an  average,  what  was  the 
per  cent  of  increase  per  year  ? 

13.  The  number  of  messages  sent  in  1870  was 
9  million;  that  sent  in  1908  was  63  million  or 
sevenfold  the  former  number.  W^hich  increased 
at  a  more  rapid  rate,  the  number  of  messages  or 
the  number  of  miles  of  line  ? 

14.  Write  messages  and  letters,  then  ascertain 
the  cost  of  sending  them  from  your  town  to  neigh- 
boring towns. 


REVIEW 
Miscellaneous  Problems 

290.  1.  One  year  the  Bureau  of  Engraving  in 
Washington  printed  over  35,000  postage  stamps  a 
minute.  If  these  stamps  are  ^  in.  long  and  are 
placed  end  to  end,  how  many  inches  long  will  the 
line  thus  formed  be  ?  How  many  feet  long  will  it 
be  ?     Yards  ? 

2.  If  these  stamps  are  -^  in.  long  and  f  in.  wide, 
how  many  square  inches  of  area  can  be  covered 
with  them  ?  How  many  square  feet  ?  How  many 
square  yards  ? 

3.  It  is  found  that,  owing  to  the  wear  of  the 
stream  upon  the  rock,  Niagara  Falls  recedes  at  the 
rate  of  4  ft.  a  year.  How  far  back  will  it  move, 
at  this  rate,  in  100  yr.  ?  How  far  has  it  moved 
during  your  lifetime  ? 

4.  If  1  cu.  ft.  of  anthracite  coal  weighs  93.5  lb., 
how  many  cubic  feet  will  weigh  3  T.? 

5.  Pressed  brick  weighs  140  lb.  per  cubic  foot. 
Find  the  weight  in  tons  of  a  brick  wall  30  ft.  long, 
12  ft.  high,  and  1^  ft.  thick. 

6.  A  cubic  foot  .of  water  weighs  62.4  lb.,  a 
cubic  foot  of   ice   weighs    57.4  lb.     What  is  the 

250 


REVIEW  251 

difference  in  weight  of  a  cubic  yard  of  ice  and  an 
equal  volume  of  water  ? 

7.  A  building  for  a  poultry  show  is  200  ft.  by 
152  ft.  How  many  feet  is  it  around  the  building  ? 
How  much  floor  space  is  there  in  the  building? 
If  there  are  over  100  exhibitors  and  half  of  the 
entire  floor  space  is  given  over  to  them,  how  much 
floor  space  may  be  assigned  to  each  ? 

8.  A  trough  is  6  ft.  long,  2  ft.  wide,  and  1  ft. 
deep.     How  many  cubic  feet  of  water  does  it  hold  ? 

9.  A  trunk  is  3  ft.  long,  2  ft.  wide,  and  1.5  ft. 
deep.     Find  its  capacity  in  cubic  feet. 

10.  A  box  is  6  in.  long,  3  in.  wide,  and  2  in. 
deep.  How  many  blocks,  of  the  shape  and  size  of 
cubic  inches,  may  be  packed  into  this  box  ? 

11.  George  rode  his  motor  cycle  for  3  hr.  at  an 
average  speed  of  27.75  mi.  an  hour.  How  far  did 
he  go? 

12.  A  schoolroom  is  9.75  yd.  long  and  8  yd. 
wide.     How  many  square   feet  in  its  floor  area  ? 

'  13.  Mr.  Jones  has  500  chickens  on  a  plot  of 
ground  150  ft.  square.  How  many  feet  of  fence 
has  he  around  the  plot  ?  How  many  square  feet 
of  area  are  there  in  the  plot  ?  How  many  square 
feet  is  this  for  every  chicken  ? 

14.  One  season  a  baseball  team  made  18  trips 
between  Chicago   and    Milwaukee.     The   railroad 


252  INTERMEDIATE  BOOK 

fare  amounted  in  all  to  $  275.40.  What  was  the 
fare  for  the  team  for  each  trip  ?  What  was  the 
fare  per  individual,  if  there  were  9  men  on 
the  team? 

15.  If  the  fare  is  $2.15  to  a  place  86  mi.  dis- 
tant, what  is  the  fare  per  mile  ? 

16.  Martha'spent  $20.15  during  the  month  of 
May.     How  much  was  this  a  day  ? 


POSITIVE   AND   NEGATIVE   NUMBERS 


Introduction 

291.  The  thermometer  commonly  used  in  Amer- 
ica is  the  Fahrenheit  (F.),  in  which  the  freezing 
point  of  water  is  marked  32°,  and 
the  boiling  point  212°. 

1.  How  many  degrees  are  there 
between  the  freezing  and  the  boil- 
ing points  of  water  ? 

2.  How  many  degrees  are  there 
between  the  freezing  point  of  water 
and  the  temperature  of  the  blood  ? 

3.  At  how  many  degrees  above  blood  tempera- 
ture does  water  boil  ? 


Water  boils 


Blood  Temc 


Water  freezes 


Fahrenheit 


Problems  in  Temperature 

292.  1.  How  much  must  the  blood  temperature 
be  reduced  to  reach  the  freezing  point  ? 

2.  If  at  2  o'clock  P.M.  the  thermometer  reads  91° 
and  is  steadily  falling  at  the  rate  of  4^°  an  hour, 
at  what  time  will  the  temperature  be  64°  ? 

3.  Between  8  a.m.  and  1  p.m.  the  mercury  rose 
from  65°  to  88°.  At  what  average  rate  per  horn- 
did  it  rise  ? 

253 


254  INTERMEDIATE  BOOK 

4.  Temperatures  below  zero  are  designated  by 

—  (minus).     For  six  mornings   in   succession    the 
temperatures  were   at    6    o'clock :    —  7°,  6°,  —  1°, 

—  10°,  4°,  —  3°.     What  was  the  average  tempera- 
ture for  these  six  mornings  ? 

5.  In  freezing  ice  cream  the  mixture  of  ice  and 
salt  reduces  the  temperature  from  60°  F.  to  28°  F. 
in  12  minutes.  What  was  the  average  drop  of 
temperature  per  minute  ? 

6.  An  animal  was  killed  and  the  carcass  put  in 
cold  storage,  where  its  temperature  was  reduced 
69|  %.      What  is  the  temperature  of  cold  storage? 

7.  At  Mobile,  Ala.,  the  average  temperature  one 
year  for  the  month  of  January  was  50°,  and  for 
the  month  of  July  80°.  The  hottest  day  in  the 
same  year  reached  102°,  the  coldest  —  1°.  Find 
the  difference  between  the  mean  temperatures  for 
January  and  July.  Find  the  difference  between 
the  extreme  temperatures  for  the  year. 

8.  Read  the  thermometer  each  hour  of  the 
school  day.  Record  and  tabulate  the  readings. 
Find  the  average  temperature. 

Temperature  Chart 

293.  This  chart  shows  the  temperatures  of  a 
patient,  taken  mornings  and  evenings  for  8  succes- 
sive days.  Such  records  often  furnish  important 
information  to  the  physician.     This  chart  shows 


POSITIVE  AND  NEGATIVE  NUMBERS        255 

not  only  how  much  the  temperature  changed,  but 
also  how  rapidly. 


Exercise  Based  on  the  Chart 

294.  1.  Read  the  temperature  for  each  day; 
estimate  the  fractions  of  degrees. 

2.  How  many  hours  intervene  between  two  suc- 
cessive readings  of  temperature  ? 

3.  On  what  day  do  you  see  the  greatest  differ- 
ence in  temperature  ? 

4.  On  what  day  the  least  ? 

5.  When  the  temperature  changes  rapidly  dur- 
ing 12  hr.,  is  the  line  connecting  the  two  tempera- 
tures steep  or  not  ? 

6.  The  line  connecting  the  two  temperatures  of 
the  second  day  is  level.     What  does  this  show  ? 

7.  Which  line  is  steeper,  the  one  for  the  first 
day  or  the  one  for  the  third?  What  does  this 
show  ? 


256 


INTERMEDIATE  BOOK 


Moonlight  Chart 

295.  This  chart  shows  the  hours  of  moonlight  on 
cloudless  nights  in  Boston,  one  year  during  June. 
One  small  space  to  the  right  stands  for  one  day ; 


Days  5 


10      15      20 
Moonlight  Chart  for  June 


25 


one  small  space  up  stands  for  one  hour.  Spaces 
from  the  bottom  line  up  to  the  heavy  top  line 
show  the  hours  of  moonlight.  There  are  about  9 
spaces  in  the  heavy  top  line,  showing  that  the 
nights  were  9  hr.  long.  On  June  5  there  were 
nearly  5  spaces  up  to  the  curved  line,  showing  that 
there  were  nearly  5  hr.  of  moonlight  during  the 
night,  if  cloudless. 


Problems  Based  on  the  Chart 

296.  1.  During  what  part  of  the  night  follow- 
ing June  5  did  the  moon  shine  ? 

2.  Find  the  number  of  hours  of  moonshine  dur- 
ing the  nights  following  June  10,  June  15,  June 
20,  June  25,  June  30. 


POSITIVE  AND  NEGATIVE  NUMBERS        257 

3.  Express  by  a  common  fraction  the  part  of 
the  night  that  was  lighted  by  the  moon  on  each  of 
these  dates. 

4.  For  each  of  these  dates  express  in  per  cent 
the  part  of  the  time  of  the  night  during  which  the 
moon  was  shining. 

5.  On  what  date  was  nearly  the  whole  night 
illuminated  by  the  moon  ? 

6.  On  what  date  was  there  practically  no 
moon? 

7.  On  what  dates  did  the  moon  shine  half  the 
night  ? 

8.  An  electric  light  company  agrees  to  supply 
street  lights  in  a  Boston  suburb  during  the  hours  of 
the  night  when  the  moon  did  not  shine,  as  shown 
by  our  chart.  How  many  hours  were  the  streets 
lighted  on  the  5th,  10th,  15th,  20th,  25th,  of 
June? 

9.  If  a  certain  district  was  lighted  at  the  rate 
of  $  1.25  an  hour,  what  was  the  cost  of  lighting  for 
each  date  named  ? 

10.  If  a  rival  company  offered  to  supply  the  same 
kind  of  light  at  15  %  less,  what  would  have  been 
the  charge  for  June  5  ? 

11.  On  what  night  was  there  no  electric  light? 
On  what  night  was  the  electric  light  on  all  the 
time? 


258  INTERMEDIATE  BOOK 

,12.  How  much  was  saved  on  the  night  of  June 
20  by  turning  off  the  electric  light  during  moon- 
light ? 

13.  By  looking  at  the  chart,  do  you  judge  that 
the  expense  of  lighting  is  reduced  to  about  l,  by 
following  the  moonlight  schedule  instead  of  an  all- 
night  schedule  ? 


DOMESTIC   POSTAGE 

297.  To  all  parts  of  the  United  States,  including 
Hawaii,  Porto  Rico,  and  the  Philippine  Islands, 
also  to  Canada,  Mexico,  and  the  Republic  of  Pan- 
ama,—  First-class  matter :  Letters  or  sealed  matter 
2j^  an  ounce  or  fraction  thereof;  this  rate  holds 
also  for  letters  to  and  from  England  and  Germany, 
postal  cards  1  ^  each  ;  with  paid  reply  card  2  ^  each. 

Second-class  matter:  Newspapers  and  other 
periodical  publications;  when  sent  by  publishers 
or  news  agents,  1  ^  per  pound  or  fraction  thereof ; 
when  sent  by  others,  1^  for  each  4  ounces  or  frac- 
tional part  thereof. 

Third-class  matter :  Books,  circulars,  pamphlets, 
proof  sheets,  or  other  printed  matter,  li^  for  each 
2  ounces  or  fractional  part  thereof,  sent  to  a  single 
address. 

Registered  matter  :  lOj^  in  addition  to  the  regular 
postage. 

Special  delivery:  V)^  in  addition  to  the  regular 
postage  of  first-class  matter. 

Written  Problems  Based  on  Rates  of  Postage 

298.  1.  How  much  postage  is  required  for  do- 
mestic letters  weighing,  respectively,  |-  oz.,  5-|-  oz., 
If  oz.,  2  oz.  ? 

269 


260  INTERMEDIATE  BOOK 

2.  A  newspaper  with  wrapper  weighs  3  oz. 
How  much  postage  must  the  publishers  pay  on 
8000  copies  ? 

3.  John  Smith  remails  one  of  these  papers. 
How  many  cents  postage  must  be  put  on  ? 

4.  George  sends  to  a  friend  a  book  weighing, 
with  wrapper,  35  oz.     How  much  is  the  postage  ? 

5.  How  many  cents  postage  are  needed  in  all 
for  mailing  to  friends  in  Canada  5  letters  weighing, 
respectively,  ^  oz.,  f  oz.,  f  oz.,  1  oz,,  ^  oz.  ? 

6.  The  Sunday  edition  of  a  paper  weighs  7  oz. 
How  much  must  the  publishers  pay  for  an  edition 
of  18,000  ? 

7.  Mrs.  Brown  sends  a  sealed  package,  weighing 
10|  oz.,  by  special  delivery.     She  pays  — —  postage. 

8.  Mary  sends  a  registered  letter,  weighing  If 
oz.,  to  a  friend  in  Hawaii.  How  much  does  she 
pay? 

9  John  mails  at  Christmas  a  book  weighing 
21|-  oz.,  a  registered  letter  weighing  ^  oz.,  and  a 
package  of  newspapers  weighing  9  oz.  How  much 
must  he  pay  in  all  ? 

10.  A  bicycle  agent  sends  out  1000  circulars  ad- 
vertising his  machines.  Each  circular  weighs  2|- 
oz.     How  much  postage  must  he  pay  altogether  ? 

11.  What  is  the  postage  on  a  letter  weighing 
3  oz.,  sent  by  special  delivery  as  registered  mail  ? 


DOMESTIC  POSTAGE  261 

The  Parcel  Post 
299.   1.   Is  Springfield,  Illinois,  nearer  to  Chicago 
than  to  Indianapolis  ? 

2.  Do  these  distances  seem  more  than  200  miles 
each  ?  Measure  the  distances  as  nearly  as  you  can 
on  the  map,  using  the  scale  of  miles  indicated  on 
the  map. 

3.  Is  Frankfort  nearer  to  Nashville  than  to 
Columbus  (Ohio)  ? 

4.  Estimate  the  following  straight-line  distances. 
Then  measure  to  see  how  close  you  come. 

Chicago  to  Nashville      Louisville  to  Wheeling 
Chicago  to  Cincinnati    Toledo  to  Indianapolis 

5.  Make  a  list  of  the  important  articles  sold  in 
the  place  in  which  you  live.  Describe  the  methods 
by  which  these  articles  are  distributed  to  neighbor- 
ing and  distant  places.  To  what  extent  is  parcel 
post  used  in  this  distribution  ? 

Merchandise,  and,  in  general,  all  matter  not  clas- 
sified in  the  United  States  postal  service  as  first, 
second,  or  third-class  matter  may  be  sent  by  United 
States  parcel  post  in  parcels  not  greater  in  size  than 
72  in.  in  length  and  girth  combined,  nor  exceeding 
in  weight  50  lb.  for  the  first  and  second  zones,  and 
20  lb.  for  the  other  zones.  The  postage  on  parcels 
varies  with  the  distance  sent,  as  is  shown  by  the 
following  table : 


262 


INTERMEDIATE  BOOK 


Table  of  Rates 


First  Zone 

Sec- 
ond 
Zone 
Eate 

Third 
Zone 
Eate 

Fourth 
Zone 
Eate 

Fifth 
Zone 
Eate 

Sixth 
Zone 
Eate 

Sev- 
enth 
Zone 
Eate 

Eighth 

Weight 

Local 
Kate 

Zone 
Rate 

Zone 
Eate 

1  pound 

$0.05 

$0.05 

$0.05 

$0.06 

$0.07 

$0.08 

$0.09 

$0.11 

$0.12 

2  pounds 

.06 

.06 

.06 

.08 

.11 

.14 

.17 

.21 

.24 

3  pounds 

.06 

.07 

.07 

.10 

.15 

.20 

.25 

.31 

.36 

4  pounds 

.07 

.08 

.08 

.12 

.19 

.26 

.33 

.41 

.48 

5  pounds 

.07 

.09 

.09 

.14 

.23 

.32 

.41 

.51 

.60 

6  pounds 

.08 

.10 

.10 

.16 

.27 

.38 

.49 

.61 

.72 

7  pounds 

.08 

.11 

.11 

.18 

.31 

.44 

.57 

.71 

.84 

8  pounds 

.09 

.12 

.12 

.20 

.35 

.50 

.65 

.81 

.96 

9  pounds 

.09 

.13 

.13 

.22 

.39 

.56 

.73 

.91 

1.08 

10  pounds 

.10 

.14 

.14 

.24 

.43 

.62 

.81 

1.01 

1.20 

11  pounds 

.10 

.15 

.15 

.26 

.47 

.68 

.89 

1.11 

1.32 

12  pounds 

.11 

.16 

.16 

.28 

.51 

.74 

.97 

1.21 

1.44 

13  pounds 

.11 

.17 

.17 

.30 

.55 

.80 

1.05 

1.31 

1.56 

14  pounds 

.12 

.18 

.18 

.32 

.59 

.86 

1.13 

1.41 

1.68 

15  pounds 

.12 

.19 

.19 

.34 

.63 

.92 

1.21 

1.61 

1.80 

16  pounds 

.13 

.20 

.20 

.36 

.67 

.98 

1.29 

1.61 

1.92 

17  pounds 

.13 

.21 

.21 

.38 

.71 

1.04 

1.37 

1.71 

2.04 

18  pounds 

.14 

.22 

.22 

.40 

.75 

1.10 

1.45 

1.81 

2.16 

19  pounds 

.14 

.23 

.23 

.42 

.79 

1.16 

1.63 

1.91 

2.28 

20  pounds 

.15 

.24 

.24 

.44 

.83 

1.22 

1.61 

2.01 

2.40 

25  pounds 

.17 

.29 

.29 

30  pounds 

.20 

.34 

.34 

40  pounds 

.26 

.44 

.44 

60  pounds 

.30 

.64 

.64 

The  local  rate  is  applicable  to  parcels  intended 
for  delivery  at  the  office  of  mailing  or  on  a  rural 
route  starting  therefrom. 

The  circles  drawn  on  our  map  have  Chicago  as 
their  centers  and  indicate  the  first,  second,  third, 
and  fourth  zones  of  distances  from  Chicago  to  other 


DOMESTIC   POSTAGE 


263 


Scale   of  Miles 


places.  Similar  circles,  drawn  upon  the  map  of  the 
entire  United  States,  showing  all  together  8  zones, 
are  used  by  clerks 
in  the  Chicago  post 
office  to  determine 
quickly  the  distances 
from  Chicago  to 
other  post  offices. 

The  post-office 
clerk  in  Nashville 
has  the  same  map 
of  the  United  States, 
but  the  circles  are 
drawn  with  their  centers  at  Nashville,  so  as  to  in- 
dicate distances  from  Nashville  to  other  places. 

Exercise  Based  on  the  Rules 

300.  Which   of   these   parcels   are   mailable   by 
parcel  post  ? 

1.  10-lb.  box,  20''  by  18''  by  10". 

2.  9-lb.  box,  18"  by  15"  by  10". 

3.  12-lb.  box,  25"  by  10"  by  8". 

4.  11-lb.  box,  30"  by  12"  by  9". 

5.  81-lb.  box,  14"  by  14"  by  14". 

Exercise  Based  on  the  Table 

301.  Compute  the  rate : 

1.  8  lb.  from  Chicago  to  Columbus  (Ohio). 

2.  11  lb.  from  Chicago  to  Louisville. 


264  INTERMEDIATE  BOOK 

3.  3  lb.  from  Nashville  to  Bowling  Green. 

4.  Get  a  rate  card  or  table  for  the  local  city. 

5.  Make  5  exercises  based  on  that  table. 

Written  Problems 

302.  1.  What  is  the  postage  on  a  parcel  weighing 
8  lb.,  sent  from  Chicago  to  Nashville  ? 

2.  What  is  the  charge  for 
sending  10  lb.  from  Chicago  to 
Cincinnati  ?     To  Aurora  ? 

3.  9  lb.  from  any  post  office 
or  delivery  on  a  rural  route  starting  from  that 
office  ? 

4.  How  much  must  a  boy  pay  in  all  for  the  fol- 
lowing parcels  which  he  mails  in  Chicago : 

8  lb.  to  be  sent  to  Pittsburgh,  Pa. 
4  lb.  to  be  sent  to  Nashville,  Tenn. 
10  lb.  to  be  sent  to  Springfield,  111. 

5.  What  is  the  combined  length  and  girth  of  a 
box  20  in.  long,  15  in.  wide,  10  in.  deep  ?  Is  it 
mailable  as  a  parcel,  if  it  does  not  exceed  the  limit 
of  weight  ? 

6.  A  parcel  is  30  in.  long  and  has  a  girth  of  35 
in.     Is  it  mailable  ? 

7.  Make  problems  based  on  the  rates  and  the 
size  of  packages  received  by  the  school. 

8.  Make  5  problems  based  on  parcel  post  deliv- 
eries for  local  industries. 


VOLUME   OR  CONTENT 

Introduction 

303.  1.  The  illustration  represents  a  cube.  It 
is  1  inch  long,  1  inch  wide,  and  1  inch  high.  Its 
contents  or  volume  is  1  cubic 
inch.  It  has  6  faces.  Is 
each  face  a  square?  How 
large  a  square? 

2.  Two  such  cubes  put 
together  form  a  prism,  2  in. 
long,  1  in.  wide,  and  1  in. 
high.  Its  volume  is  2  cubic 
inches. 

3.  If  three  such  cubes  are  put  together  in  one 
row,  they  make  a  prism  2  in.  long,  1  in.  wide,  and 
1  in.  high.     Its  volume  is  2  cubic  inches. 

4.  If  2  such  prisms,  each  3  in.  long,  are  put 
side  by  side,  they  form  together  a  new  prism,  3  in. 
long,  2  in.  wide,  and  1  in.  high.  How  many  cubic 
inches  in  that  new  prism? 

5.  The  edge  stands  for  1  yard.  How  many 
feet  does  ^  of  that  line  stand  for? 

6.  This  drawing  is  a  cube  1  yd.  or  3  ft.  long, 
wide,  and  high.    How  many  square  feet  are  there  in 

265 


266 


INTERMEDIATE  BOOK 


one  face  of  this  cube?     The  cube  is  divided  into 
smaller  cubes,  each  1  ft.  on  a  side  and  each  a  cubic 

foot.  How  many  cubic  feet 
do  you  see  in  the  front  layer 
of  the  large  cube? 

7.  If  there  are  9  cubic 
feet  in  the  front  layer,  how 
many  are  in  the  layer  just 
back  of  it  ?  How  many  in 
the  last  layer? 

8.  How  many  cubic  feet  in  the  entire  large 
cube?     How  many  cubic  feet  in  a  cubic  yard? 

9.  You  see  that  27  is  the  product  of  3,  3,  and  3. 
If  you  had  a  prism  3  in.  long,  2  in.  wide,  and  3  in. 
high,  how  many  cubic  inches  would  there  be  in  it? 

10.  How  many  1-inch  cubes  can  be  packed  in  a 
box,  4  in.  long,  3  in.  wide,  and  2  in.  deep  ? 

11.  A  merchant 
has  boxes  1  ft.  each 
way.  How  many 
such  boxes  can  be 
packed  in  a  trunk 
3  ft.  long,  2  ft. 
wide,  and  2  ft. 
deep? 

12.  The     draw- 


ing,  as    a   whole. 


12  in. 


VOLUME  OR  CONTENT  267 

stands  for  a  cubic  foot.  How  many  inches  long, 
wide,  and  high  is  a  cubic  foot?  Imagine  it  made 
up  of  1-inch  cubes.  How  many  cubic  inches  in 
the  bottom  layer? 

13.  The  other  layers  are  not  drawn.  Imagine 
them  drawn.  How  many  layers  are  there,  includ- 
ing the  bottom  layer? 

14.  If  there  are  12  layers,  and  each  layer  con- 
tains 144  cubic  inches,  how  many  cubic  inches  are 
there  in  a  cubic  foot? 

Cubic  Measure 
304.   Memorize  the  table. 


TABLE   OF   CUBIC  MEASURE 

1728  cubic  inches  (cu.  in.)  =  1  cubic  foot  (cu.  ft.) 
27  cubic  feet  =  1  cubic  yard  (cu.  yd.) 


In  this  table  these  relations  are  established: 

Length        Width         Height  Volume 

in.  X  in.  x  in.  =  cu.  in. 
ft.  X  ft,  X  ft.  =  cu.  ft. 
yd.   X    yd.  x  yd.   =    cu.  yd. 

Oral  Problems 

305.  1.  How  many  1-inch  cubes  can  be  packed 
into  a  box  12  in.  on  an  edge? 

2.  The  contents  of  a  tank  is  1  cu.  yd.  A  bucket 
can  hold  exactly  1  cu.  ft.  of  water.  How  many 
bucketfuls  will  hll  the  tank? 


268  INTERMEDIATE  BOOK 

3.  A  bin  is  2  ft.  by  3  ft.  by  4  ft.  Does  it  hold 
more  than  a  cubic  yard,  or  less  ? 

4.  A  box  is  20  in.  by  10  in.  by  9  in.  Does  it 
hold  more  than  1  cu.  ft.,  or  less? 

5.  How  many  cubic  yards  of  air  can  a  school- 
room 10  yd.  long,  10  yd.  wide,  and  3  yd.  high  hold? 

6.  A  man  starts  to  dig  a  trench  5  ft.  by  3  ft.  by 
2  ft.  How  many  cubic  feet  of  earth  must  he  re- 
move? 

7.  Take  a  candy  box  and  estimate  how,  long, 
wide,  and  deep  it  is.  How  many  cubic  inches  in  its 
contents  ?  How  many  square  inches  in  the  bottom  ? 
The  sides  ?     The  ends  ? 

8.  Make  a  paper  box  2  in.  long,  1  in.  wide,  and 
1  in.  deep.     How  many  1-inch  cubes  will  it  hold  ? 

9.  A  coal  bin  is  10  ft.  by  4  ft.  by  3  ft.  How 
many  cubic  feet  of  coal  will  it  hold  ?  How  many 
square  feet  of  boards  are  there  in  each  of  the  2  sides 
of  the  bin  ?  In  each  of  the  2  ends  of  the  bin  ?  In 
both  sides  and  both  ends  taken  together  ? 

10.    Make  an  oral  problem  based  on  the  table. 


Written  Exercise 

306.    Find  the  volume  of 

a  prism 

: 

1. 

2. 

3. 

4. 

5. 

Length    12  in. 

15  ft. 

20  in. 

17  m. 

10  ft. 

Breadth     7  in. 

5  ft. 

7  in. 

12  in. 

9  ft, 

Thickness  6  in. 

31  ft. 

5fin. 

4|in. 

5|ft. 

VOLUME  OR  CONTENT 


269 


Written  Problems 

307.  1.  A  bin  is  7  ft.  by  4  ft.  by  3  ft.  How 
much  more  will  it  hold  than  2  cu.  yd.  ? 

2.  A  box  is  12  in.  long,  9  in.  wide,  and  5  in. 
deep.     How  much  less  than  1  cu.  ft.  does  it  hold  ? 

3.  How  many  cubic  feet  of  earth  were  removed 
in  digging  a  cellar  15  ft.  long,  13  ft.  wide,  and  7 
ft.  deep? 

4.  How  much  larger  is  a  box  10  ft.  by  5  ft.  by 
3  ft.  than  a  box  6  ft.  by  6  ft.  by  4  ft.  ? 

5.  Which  holds  more,  a  box  6  in.  by  4  in.  by 
2  in.  or  one  5  in.  by  4  in.  by  3  in.  ? 

6.  How  many  1-foot  cubes  are  equal  to  a  2-foot 
cube  (a  cube  2  ft.  on  an  edge)  ?  To  a  3-foot  cube  ? 
To  an  11-foot  cube? 

7.  How  many  eggs  are  there 
in  the  upper  layer  of  the  top 
box? 

8.  Each  box  has  two  such 
layers  of  eggs.  How  many  eggs 
in  each  box  ?  How  many  in 
all  three  boxes  ? 

9.  How  many  dozen  eggs  in 
one  box  ?     In  all  three  ? 

10.    What  is  each  box  worth  when  eggs  are  22^^ 
a  dozen  ? 


270 


INTERMEDIATE  BOOK 


11.  A  merchant  received  13  such  boxes  and  sold 
them  at  28^^  a  dozen  eggs.  How  much  money  did 
he  take  in  ? 

12.  A  brick  is  8  in.  long,  4  in.  wide,  and  2  in. 
thick.     How  many  cubic  inches  in  it  ? 

13.  How  many  such  bricks  does  it  take  for  a 
cubic  foot  ? 

14.  A  brick  wall  is  5  ft.  by  3  ft.  by  1  ft.  How 
many  bricks  are  there  in  it  ? 

15.  How  long  a  wall  4  ft.  high  and  li  ft.  thick 
can  be  built  with  972  bricks  ? 

16.  A  tinsmith  is  making  a  water  tank,  without 
cover.  The  tank  is  6  ft.  long,  4  ft.  wide,  and  5  ft. 
deep.     How  many  square  feet  of  tin  does  he  use  ? 

17.  How  many  cubic  feet  will  it  hold  ?  Allow- 
ing 62J  lb.  to  a  cubic  foot  of  water,  how  many 

pounds  of  water  will  the 
tank  hold?  How  much 
more  is  it  than  3  T.  ? 

18.  Find  the  number  of 
square  inches  in  the  entire 
surface  of  a  2-inch  cube. 

Cut  thin  cardboard  into 
the  shape  of  the  drawing 
shown  here.  Make  a  2-inch 
cube.  Paste  together  the 
free  edges  by  using  stickers 
for  mounting  stamps. 


2  m. 

2  in. 

2  in. 


VOLUME  OR  CONTENT  271 

19.  Find  the  number  of  cubic  inches  in  this 
2-inch  cube. 

20.  Find  the  area  of  the  surface  of  a  box  and 
cover  15  in.  long,  5|^  in.  wide,  and  2^  in.  high. 
Find  also  its  volume. 

21.  A  strawberry  box  is  6''  long,  4''  wide,  and 
4''  deep.  How  many  such  boxes  can  be  packed 
in  a  case  2^'  long,  1|^'  wide,  and  |'  deep  ? 

22.  A  rectangular  water  trough  is  4  ft.  long, 
1  ft.  wide,  and  ^  ft.  deep.  How  many  gallons  of 
water  will  it  hold,  if  there  are  231  cu.  in.  in  a 
gallon  ? 

23.  One  cubic  yard  of  earth  makes  one  load. 
How  many  loads  are  necessary  to  fill  up  an  old 
cellar  15  ft.  by  10  ft.  by  6  ft.  ? 

24.  A  wagon  box  is  9  ft.  long,  3  ft.  wide,  and 
1  ft.  deep.  How  many  times  will  this  be  filled 
with  earth  in  digging  a  cellar  21  ft.  by  9  ft.  and  7 
ft.  deep  ? 

25.  A  boy  split  enough  kindling  to  make  a  pile 
6  ft.  long,  1  ft.  wide,  and  3  ft.  high.  What  part  of 
a  cord  did  he  split  ? 

26.  A  water  trough  holds  15  gal.  of  water. 
It  is  14  in.  wide  and  11  in.  deep.     Find  its  length. 

27.  If  36  cu.  ft.  of  coal  weigh  a  ton,  what  is  the 
weight  of  a  wagon  load  9  ft.  long,  3 J  ft.  wide  and 
3  ft.  deep? 


REVIEW 

Oral  and  Written  Problems 

308.  Study  each  problem.  Write  an  answer  that 
is  approximately  the  answer  to  that  problem.  Solve 
the  problems  and  notice  what  answers  are  approxi- 
mately correct. 

1.  If  it  takes  7  men  35f  da.  to  do  a  piece  of 
work,  how  long  will  it  take  1  man  ? 

2.  Add  15|,  lOf,  25i,  30.6,  20.2. 

3.  How  many  feet  in  120.56  yd.  ? 

4.  Express  as  a  decimal  fraction  67|^%. 

5.  Express  as  a  common  fraction  175%. 

6.  Find  percentage  on  $2609  at  19%. 

7.  A  fruit  raiser  planted  260  trees.     13  died. 
What  per  cent  died  ? 

8.  Of  360  pupils,  18  are  absent.     What  per 
cent  are  absent  ? 

9.  1000  lb.  of  sea  water  contains  36  lb.  of  salt. 
What  per  cent  is  salt  ? 

10.  Mr.  Hunt  borrows  money  at  6  %  and  pays 
$  25  interest  annually.     How  much  did  he  borrow  ? 

11.  If  5  per  cent  of  a  number  is  8.3,  what 
is  the  number  ? 

272 


REVIEW 


273 


12.  What  per  cent  of  a  pound  are  9  ounces  ? 

13.  A  man  spends  10|-%  of  his  earnings  for 
board.  He  pays  $  260  a  year  for  board.  How  much 
does  he  earn  ? 

14.  A  merchant  sold  a  piano  for  $  450  that  cost 
him  $  400.     What  per  cent  of  the  cost  did  he  gain  ? 

15.  93.08  is  26  %  of . 

16.  1753  is  what  per  cent  of  3506  ? 

17.  What  per  cent  of  a  square  foot  are  80  sq.  in.  ? 

18.  What  per  cent  of  a  mile  are  81  rods  ? 


Written  Problems 

309.   1.    How  long  and  wide  is  one  side  of  the 
roof  of  this  barn  ? 


24 


2.  Snow  2  ft.  deep  has  a  weight  of  about 
12  lb.  per  square  foot.  How  much  pressure  will 
2  ft.  of  snow  exert  on  the  two  sides  of  the  roof 
of  this  barn? 


274  INTERMEDIATE  BOOK 

3.  It  takes  about  1000  shingles  to  make  100  sq. 
ft.  of  roof.  If  a  bunch  of  shingles  contains  250 
shingles,  how  many  bunches  are  needed  for  this 
roof?  For  a  fraction  of  a  bunch,  take  a  whole 
bunch. 

4.  If  a  bunch  of  shingles  sells  at  97^,  find  the 
cost  of  the  shingles  for  this  roof. 

5.  If  more  of  each  shingle  is  exposed  to  the 
weather,  so  that  only  800  shingles  are  needed  per 
100  sq.  ft.,  what  is  the  cost  of  the  shingles  for  this 
roof? 

6.  When  a  roof  is  to  be  covered  with  slates  6  in. 
by  12  in.,  builders  use  about  500  slates  per  100  sq. 
ft.     How  many  slates  will  be  needed  for  this  roof  ? 

7.  The  triangular  part  of  each  end  of  the  build- 
ing, close  to  the  roof,  called  the  gable,  is  24'  along 
the  base  and  9'  high.     Find  its  area. 

8.  If  a  very  strong  wind  blows  squarely  against 
the  end  of  the  barn  and  exerts  a  pressure  of  14  lb. 
per  square  foot,  what  is  the  entire  pressure  against 
the  end  of  the  building  ? 

9.  Find  the  cost  of  painting  the  sides  of  the  barn 
at  23^  per  square  yard. 

10.  What  is  the  cost  of  painting  the  roof  at  19^ 
per  square  yard  ? 

11.  Would  the  bill  have  been  more  or  less,  if  the 
painting  of  the  whole  barn  had  been  done  at  21|^^ 
a  square  yard  ? 


REVIEW 


275 


12.  If  the  building  had  been  erected  of  brick,  and 
14  bricks  had  been  used  for  each  square  foot  of 
outside  surface,  what  would  have  been  the  bill  for 
brick,  at  $  6  per  thousand  brick  ? 

13.  How  much  greater  would  the  expense  have 
been,  if  the  brick  wall  had  been  built  thicker,  so  as 
to  require  22  bricks,  instead  of  14,  for  a  square 
foot  of  outside  surface  ?  In  what  ratio  is  the  new 
cost  to  the  old  ? 

14.  How  many  cubic  yards  of  space  are  there  in 
this  barn  from  the  ground  floor  up  to  the  gables  ? 

15.  If  well-settled  timothy  hay  runs  about 
360  cu.  ft.  to  the  ton,  how  many  tons  of  hay  will 
the  barn  hold  when  filled  up  to  the  gables  ? 

16.  If  loose  timothy  hay  runs  about  450  cu.  ft. 
to  the  ton,  how  many  tons  of  it  will  the  barn  hold 
when  filled  up  to  the  gables  ? 


Written  Problems 


310.  1.  The  cor- 
ner stone  of  the  Cap- 
itol at  Washington 
was  laid  Sept.  18, 
1788.  Exactly  how 
long  ago  was  tliat  ? 
2.  The  old  dome 
was  removed  in 
1856  and  the  present 


276  INTERMEDIATE  BOOK 

dome  completed  in    1865.     Find  the  age  of   the 
new  dome. 

3.  The  capitol  stands  on  a  plateau  88  ft.  above 
the  level  of  the  Potomac  River.  The  height  of  the 
dome  above  the  ground  is  287  ft.  5  in.  The  statue 
of  Freedom  is  19  ft.  6  in.  tall.  How  high  above 
the  ground  is  the  head  of  the  statue  ?  How  far 
above  the  Potomac  is  it  ? 

4.  The  Metropolitan  Life  Insurance  Building  in 
New  York  City  is  700  ft.  3  in.  high.  How  much 
higher  is  it  than  the  National  Capitol  ? 

5.  The  Metropolitan  Life  is  275  ft.  3  in.  long 
and  123  ft.  5  in.  wide.  The  area  covered  by  the 
United  States  capitol  building  is  153,112  sq.  ft. 
How  many  square  feet  larger  is  the  area  of  the 
latter  ?     How  many  times  larger  is  it  ? 

6.  The  capitol  is  751  ft.  4  in.  long,  its  maximum 
width  is  350  ft.  If  this  width  were  uniform,  how 
many  square  feet  would  the  area  exceed  its  present 
actual  area  of  153,112  sq.  ft.? 

7.  The  dome  is  of  iron  and  weighs  8,009,200 
pounds.     Reduce  this  to  tons. 

8.  The  bronze  statue  of  Freedom  weighs  14,985 
pounds.  If  bronze  is  8.45  times  heavier  than  wood, 
what  would  be  the  weight  of  a  wooden  statue  of 
the  same  dimensions  ? 


REVIEW  277 

9.  The  Senate  chamber  is  113  ft.  long,  80  ft. 
wide,  and  36  ft.  high.  Find  the  number  of  cubic 
yards  of  space  in  it. 

10.  The  Representatives'  Hall  is  139  ft.  long, 
93  ft.  wide,  and  36  ft.  high.  How  many  cubic 
yards  of  space  in  it  ? 

11.  The  capitol  covers  an  area  of  153,112  sq.  ft. 
How  many  acres  is  this  in  round  numbers  ? 

12.  The  building  of  the  Library  of  Congress  covers 
3|-  acres.  Is  this  more  than  the  area  of  the  capitol? 
Find  the  difference  in  square  feet. 

13.  The  site  of  the  library  building  is  10  acres. 
What  per  cent  of  it  is  taken  up  by  the  building 
itself?  Find  the  ratio  of  the  part  of  the  site  occu- 
pied by  the  building  to  the  whole  site. 

14.  The  floor  space  in  all  parts  of  the  building, 
taken  together,  is  326,195  sq.  ft.  How  many  square 
feet  less  than  8  A.  is  this  ? 

15.  The  book  stacks  contain  56  mi.  of  shelving. 
How  many  shelves,  each  4  ft.  long,  furnish  this 
amount  of  shelving  ? 

16.  How  long  would  it  take  you  to  travel 
56  miles  on  a  bicycle  at  the  rate  of  9  miles  an 
hour? 

17.  The  service  of  the  library  consists  of  236 
employees  in  the  library  proper,  70  for  copyright, 
25  for  distribution  of  cards,  5  for  law  indexing. 


278  INTERMEDIATE  BOOK 

127  for  care  of  building  and  grounds.  How  much, 
less  is  this  than  the  total  number  of  the  members 
of  Congress,  there  being  96  senators  and  391 
representatives  ? 

Written  Exercises  and  Problems 

311.  1.  How  many  cubic  inches  in  a  peck,  if 
there  are  2150.4  cu.  in.  in  a  bushel  ? 

2.  How  many  cubic  inches  in  a  pint,  if  there 
are  231  cu.  in.  in  a  gallon? 

3.  A  liquid  quart  is  less  than  a  dry  quart,  con- 
taining only  57f  cu.  in.,  while  the  dry  quart  con- 
tains 67|-  cu.  in.  Find  the  difference  between  the 
two. 

4.  Find  the  area  of  a  table  5  ft.  7  in.  long  and 
4  ft.  5  in.  wide. 

5.  The  area  of  a  drawing  board  is  7  sq.  ft.  72 
sq.  in.     Its  length  is  3  ft.  4  in.     Find  its  width. 

312.  Find  the  missing  part  in  each  of  the  follow- 
ing surfaces: 


Figure 

Base 

Height 

Area 

1. 

Rectangle 

2  ft.  3  in. 

1  ft.  4  in. 

2. 

Rectangle 

10  ft.  2  in. 

1  ft.  6  in. 

3. 

Rectangle 

5  ft.  6  in. 

2  ft.  3  in. 

4. 

Rectangle 

2  ft.  6  in. 

3 

sq. 

ft.  18  sq.  in. 

5. 

Triangle 

3  ft.  6  in. 

2  ft.  4  in. 

6. 

Triangle 

4  ft.  7  in. 

3  ft.  2  in. 

7. 

Rectangle 

3  ft.  6  in. 



11 

sq. 

ft.  96  sq.  in. 

REVIEW 


279 


Written  Problems 

313.  1.  Find  the  volume  in  cubic  feet  of  a  box 
3  ft.  2  in,  long,  2  ft.  1  in.  wide,  and  1  ft.  6  in. 
high. 

2.  Find  the  number  of  cubic  feet  of  space  in  a 
trunk  2  ft.  6  in.  long,  1  ft.  6  in.  wide,  and  1  ft. 
8  in.  deep. 

3.  Which  trunk  holds  more,  one  that  is  2  ft. 
8  in.  long,  1  ft.  8  in.  wide,  and  1  ft.  7  in.  deep,  or 
one  that  is  2  ft.  6  in.  long,  1  ft.  11  in.  wide,  and 
1  ft.  4  in.  deep?  What  is  the  difference  in 
volumes  ? 

4.  If  a  ton  of  coal  occupies  36  cu.  ft.,  how 
many  tons  of  coal  will  a  bin  8'  x  4'  x  6'  hold  ? 

5.  Coal  is  bought  by  the  long  ton  (2240  lb.) 
and  sold  by  the  short  ton  (2000  lb.).  How  many 
long  tons  does  it  take  to  gain  one  short  ton  ? 

Table  for  Reference 

314.  Weight  and  Cost  of  Railroad  Cars 


Type  of  Cab 

Weight 
IN  Lb. 

Capacity 

Length 

Width 

Height 

Cost 

Wood  Box 

37,000 

80,000  lb. 

36  ft. 

8  ft.  6  in. 

8  ft. 

$1,100 

steel  Coal 

42,000 

100,000  lb. 

31ft. 

9  ft.  4  in. 

7  ft.  6  in. 

1,200 

Flat 

32,000 

80,000  lb. 

41ft. 

9  ft.  2  in. 

950 

Day  Coach 

85,000 

68  passengers 

60  ft, 

8  ft.  10  in. 

9  ft. 

9,000 

Parlor  Car 

105,000 

34  passengers 

70  ft. 

8  ft.  6  in. 

9  ft.  6  in. 

15,500 

Sleeping  Car 

115,000 

27  berths 

72  ft.  6  in. 

8  ft.  6  in. 

9  ft.  6  in. 

19,000 

280  INTERMEDIATE  BOOK 

Problems  Based  on  the  Table 

315.  1.  Nine  empty  wood  box  cars  are  discon- 
nected from  a  freight  train.  In  their  place  8  empty 
steel  coal  cars  are  added  on.  How  much  heavier  is 
the  train  now  ? 

2.  Passengers  weigh  150  lb.  on  an  average. 
Which  is  heavier,  a  day  coach  full  of  passengers  or 
a  parlor  car  full  of  passengers  ?  What  is  the 
difference  in  weight  ? 

3.  If  two  trains  travel  on  the  same  route  and 
with  the  same  speed,  which  needs  a  more  powerful 
locomotive,  the  train  with  4  flat  cars,  5  steel  cars, 
and  10  wood  box  cars,  or  the  train  with  11  flat 
cars,  4  steel  coal  cars,  and  7  wood  box  cars,  each 
car  in  both  trains  being  loaded  to  its  full  capacity  ? 

4.  Find  the  floor  area  of  a  wood  box  car. 

(Instead  of  reducing  feet  to  inches  and  then  finding 
the  number  of  square  inches,  it  is  easier  in  this  case  to 
take  8  ft.  6  in.  (8.5  ft.)  and  compute  the  number  of 
square  feet.) 

5.  How  much  less  is  the  floor  area  of  a  coal  car 
than  of  a  box  car  ? 

6.  How  much  greater  is  the  floor  area  of  a 
parlor  car  than  the  floor  area  of  a  day  coach  ? 

7.  Which  has  a  larger  capacity,  a  coal  car  or  a 
box  car  ? 

(Take  8  ft.  6  in.=  8.5  ft.  ;  7  ft.  6  in.=  7.5  ft.;  9  ft. 
6  in.  =  9.5  ft.) 


REVIEW  281 

8.  Find  the  number  of  cubic  feet  of  space  for 
each  passenger  in  a  day  coach. 

9.  Find  the  dimensions  of  your  schoolroom, 
also  the  number  of  pupils  in  it.  See  whether  the 
space  allowance  for  each  pupil  exceeds  that  of  a 
passenger  in  a  day  coach.     What  is  the  difference? 

10.  Why  does  a  passenger  in  a  parlor  car  pay 
more  than  one  in  a  day  coach  ?  How  many  cubic 
feet  of  space  are  allowed  for  each  in  a  parlor  car  ? 

11.  How  many  cubic  feet  are  allowed  for  each 
berth  in  a  sleeping  car  ? 

12.  Compute  the  cost  of  the  car  and  locomotive 
equipment  of  a  train  made  up  of  8  day  coaches, 
2  parlor  cars,  and  5  sleepers,  and  pulled  by  a  Pacific 
type  locomotive  costing  $  18,700. 

13.  If  a  Mogul  locomotive  costs  28  %  less  than 
one  of  the  Pacific  type,  find  the  cost  of  the  former, 
when  the  latter  is  $  18,700. 

14.  What  is  the  ratio  of  the  cost  of  a  coal  car  to 
that  of  a  box  car  ? 

15.  What  is  the  ratio  of  the  cost  of  a  day  coach 
to  the  cost  of  a  sleeping  car  ? 

Since  9000  :  19000  =  9  :  19,  we  may  say  that  the  ratio 
required  is  as  9  is  to  19. 

16.  Show  that  the  cost  of  a  parlor  car  is  to  the 
cost  of  a  flat  car  as  310  is  to  19,  or,  approximately, 
as  16  is  to  1. 


282  INTERMEDIATE  BOOK 

17.  An  electric  locomotive  used  on  one  road 
weighs  160,000  lb. ;  that  used  on  another  road 
weighs  180,000  lb.  Find  the  ratio  of  the  first 
weight  to  the  second. 

Written  Exercise 
316.    Write  in  the  Arabic  notation  : 

1.  lY,  Y,  VI,  VII,  VIII,  IX,  XI,  XII. 

2.  XIII,  XVI,  XIV,  XXI,  XXV,  XXIV, 
XXIX. 

3.  LX,  LXV,  LXIV,  MC,  MCC,  MCCC. 

Write  in  the  Roman  notation : 

4.  13,  14,  17,  18,  19,  20,  30. 

5.  36,  47,  54,  69,  99,  95,  96. 

6.  94,  200,  500,  600,  400,  1100. 


GENERAL   REVIEW 

Addition  Combinations 

317.    Add  quickly.     Practice  until  the  additions 
can  be  made  perfectly  without  hesitation. 


1. 

Group  I. 
Group  II. 
Group  III. 
Group  IV. 

2    4    9    2    5 
2    9    3    3    4 

3  6  8  6  9 
6    2    2    3    4 

2. 

4    2    8    7    5 
4    4    6    3    8 

5  8  5  7  3 
2    7    5    6    5 

3. 

2    6    9    8    9 
7    6    7    4    9 

3  5    9    7    9 

4  7    17    2 

4. 

6    5    8    18 
9    6    8    7    9 

5  12  8  7 
9    8    13    1 

When  these  combinations  are  perfectly  mas- 
tered, the  addition  of  larger  numbers  may  be  made 
familiar  by  adding  10  to  each  number  in  the  lower 
line.  Then  20,  30,  and  so  to  100  may  be  added. 
Thus  in  the  second  group  the  lower  row  of  figures 
will  be  14,  14,  16,  etc. 

Oral  Exercise 

318.  Add  columns  of  numbers  from  3  to  10  and 
higher.  These  columns  may  be  extended  to  cor- 
respond with  the  usual  length  of  columns  in 
business. 


284  INTERMEDIATE  BOOK 

1.  2.  3.  4.  5.  6.  7.  8.  9. 


6 

5 

4 

3 

2 

2 

6 

3 

7 

4 

3 

9 

3 

8 

6 

9 

3 

4 

3 

4 

5 

8 

3 

9 

7 

5 

6 

2 

2 

3 

8 

3 

5 

4 

2 

7 

1 

4 

6 

2 

4 

2 

6 

9 

4 

8 

8 

4 

5 

7 

9 

3 

2 

5 

3 

5 

3 

8 

2 

3 

6 

3 

4 

9 

2 

4 

3 

6 

4 

2 

8 

5 

3 

When  this  exercise  has  been  drilled  sufficiently, 
begin  with  12,  14,  23,  26,  .  .  .  98,  103,  etc.,  in 
place  of  the  2,  4,  3,  6,  etc.,  the  first  line  in  each 
column,  to  train  in  the  addition  of  larger  numbers. 

Another  step  is  necessary  to  secure  the  practical 
skill  required  in  daily  transactions. 

319.  Since  members  of  two  or  more  figures  are 
met  in  everyday  business,  the  ability  to  carry  in 
addition  is  indispensable.  Teachers  may  form 
such  columns  of  numbers  of  two,  three,  four,  and 
more  figures,  and  train  pupils  to  add  them  with 
accuracy  at  optimum  rate  of  speed. 

Later  it  is  well  to  follow  usual  method  of  add- 
ing (and  subtracting)  in  making  change  in  money 
transactions.  It  is  not  too  much  to  expect  pupils 
to  add  numbers  of  two  and  even  three  figures,  in 


REVIEW  285 

money  terms,  as  high  as  $100.00.  Thus  pupils 
will  readily  learn  to  add:  13  +  12  +  25  +  10  +  15 
+  25  as  13,  25,  50,  60,  75,  100.  They  do  this  in 
money  and  should  readily  carry  the  power  over  to 
related  exercises.  Exercises  should  be  formed  to 
complete  as  far  as  possible  pupils'  skill  in  such  addi- 
tion.   The  following  columns  may  be  suggestive. 


10. 

11. 

12. 

13. 

42 

14. 

18 

16 

47 

26 

65 

22 

28 

32 

43 

44 

13 

35 

24 

72 

51 

74 

52 

46 

25 

36 

26 

68 

24 

46 

72 

18 

27 

35 

87 

39 

15. 

16. 

17. 

18. 

27 

46 

507 

213 

52 

73 

351 

625 

24 

32 

112 

143 

62 

45 

214 

432 

27 

81 

315 

107 

43 

36 

421 

634 

56 

65 

137 

210 

286  INTERMEDIATE  BOOK 

320.  Exercises  may  be  brought  into  close  agree- 
ment with  actual  practice  in  money  transactions 
by  making  problems  involving  numbers  as  follows  : 

1.  2.  3.  4.  5. 

$2.00  .25  $1.00 

.50        $10.00           2.00  .25  2.00 

.25               .50            .25  .15  .50 

.10               .25             .25  .03  .25 

.15               .25             .50  .32  1.25 


6. 

7. 

8. 

9. 

.50 

.25 

$5.00 

$15.00 

$25.00 

.05 

1.00 

.25 

12.50 

.01 

.25 

2.75 

.05 

2.19 

3.75 

3.00 

.20 

Addition  Exercise 

321.   Add  the  columns  beginning  at  the  bottom, 
test  by  adding  down,  time  both  methods : 

1.  2.  3.  4. 

25  96  93  48 

87  81  33  84 

42  25  62  53 

67  37  41  79 

66  44  67  67 

89  66  88  75 

23  75  72  56 

34  89  12  94 


REVIEW 

5. 

6. 

7. 

8. 

21 

57 

13 

69 

46 

22 

42 

32 

59 

45 

86 

45 

60 

73 

47 

67 

83 

19 

23 

33 

49 

64 

55 

71 

27 

38 

63 

90 

68 

43 

92 

64 

45 

37 

77 

287 


Make  new  exercises  by  rearranging  the  addends. 


Addition  Exercise 

322.  Add  by  columns,  then  by  rows  across  the 
page.  Find  the  total  sum  of  the  numbers  by 
each  method. 


1. 

2. 

3. 

$3.25 

.75 

.23 

.76 

1.50 

1.48 

1.19 

2.20 

2.25 

.29 

.65 

.55 

.98 

9.35 

1.75 

.85 

6.89 

6.80 

7.63 

2.19 

.49 

.84 

3.20 

1.98 

1.25 

1.15 

8.75 

288  INTERMEDIATE  BOOK 


3tice  addition 

across  the  page. 

It  is  a  form 

ccurs  often  in 

business. 

4. 

5. 

6. 

12.65 

75.15 

31.15 

23.40 

6.27 

16.25 

69.25 

8.95 

6.15 

46.37 

6.45 

2.50 

6.55 

45.60 

50.67 

14.75 

16.27 

25.18 

42.20 

24.15 

7.75 

6.49 

6.95 

1.50 

7.25 

35.45 

62.35- 

Addition  Exercise 
323.   Add.     Try  to  shorten  time  by  practice : 


1. 

2. 

3. 

4. 

11 

65 

26 

73 

22 

32 

55 

84 

64 

14 

14 

23 

71 

23 

27 

46 

19 

57 

64 

17 

36 

91 

86 

29 

49 

38 

95 

31 

53 

45 

37 

72 

27 

63 

84 

18 

82 

72 

25 

65 

14 

49 

60 

94 

15 

77 

42 

73 

REVIEW 

5. 

6. 

7. 

8. 

18 

132 

346 

456 

27 

640 

220 

634 

33 

309 

614 

581 

48 

246 

325 

790 

62 

125 

675 

688 

12 

670 

806 

857 

19 

87 

642 

435 

21 

75 

614 

506 

67 

42 

126 

783 

85 

369 

350 

658 

94 

401 

623 

743 

33 

625 

847 

387 

72 

72 

637 

961 

24 

155 

949 

203 

289 


Dictation  Exercise 

324-  Write  from  dictation  and  add.  Time  your- 
self in  addition. 

Test  accuracy  and  speed  by  adding  from  top  to 
bottom. 


1. 

2. 

3. 

4. 

423 

231 

186 

301 

576 

147 

724 

810 

962 

376 

476 

256 

128 

312 

352 

100 

634 

732 

471 

403 

246 

673 

524 

719 

107 

132 

289 

322 

290  INTERMEDIATE  BOOK 


5. 

6. 

7. 

8. 

523 

2376 

8361 

34,562 

879 

2837 

5496 

18,649 

391 

1549 

8067 

43,786 

418 

3412 

2952 

83,245 

573 

5835 

1694 

52,837 

726 

8043 

7209 

29,004 

607 

1979 

3573 

37,561 

9. 

10. 

11. 

S  5640.71 

$1831 

$45| 

3763.89 

376 

125i 

2163.25 

214| 

212^ 

7189.66 

8651 

320 

3548.75 

4611 

404| 

2762.57 

329 

5161 

1836.12 

105i   ' 

75 

Addition  Exercise 

325.  Add. 

Test! 

by  adding  down  columns. 

12. 

13. 

14. 

96,423 

47,485 

76,423 

8,402 

3,689 

89,845 

6,075 

62,549  . 

6,505 

8,941 

8,632 

92,861 

6,243 

4,815 

14,650 

8,655 

6,842 

19,425 

75,242 

95,586 

6,307 

68,115 

3,704 

25,642 

REVIEW 

291 

15. 

16. 

17. 

96,500 

98,424 

156,742 

6,270 

16,821 

68,045 

8,964 

42,461 

784,924 

53,825 

53,119 

61,075 

6,403 

55,427 

42,740 

8,947 

43,862 

312,625 

13,425 

31,465 

61,842 

6,854 

55,408 

37,896 

1,521 

87,623 

896,420 

680,425 

62,576 

7,256,748 

36.017 

119,214 

847,223 

62,422 

35,560 

67,895 

119,627 

125,225 

967,425 

869,421 

67,580 

5,564,261 

Subtraction  Exercise 
326.    Subtract : 

1.  2.  3.  4. 

$156.47  75.89  97.14  76.15 

3.29  15.62  38.25  6.27 


8. 

1914 
1775 


5. 

6. 

7. 

86.05 

69.11 

1915 

14.20 

15.27 

1492 

9. 

10. 

11. 

1912 

1492 

1900 

1366 

850 

1399 

12. 

1912 
1792 


292  INTERMEDIATE  BOOK 

Subtraction  Exercise 
327.  Subtract  the  number  at  bottom  of  each 
column,  from  each  of  the  numbers  of  the  column. 
Time  yourself  for  each  column.  Repeat  until  you 
can  do  them  unhesitatingly  and  accurately.  How 
much  time  can  you  gain  from  practice  ? 


1. 

2. 

3. 

487,205 

125,786 

6.14 

67,481 

78,543 

115. 

695,560 

86,491 

69.75 

72,897 

196,325 

4.689 

846,423 

477,584 

32.12 

952,843 

673,962 

6.23 

65,896 

425,759 

82.04 

712,872 

153,861 

3.006 

49,753 

75,708 

2.375 

4. 

5. 

6. 

9.2 

72.3 

175.00 

14.03 

150.605 

87.82 

6.152 

53.715 

325.45 

35.005 

29.45 

4575.00 

8.141 

43.007 

500.00 

6.007 

21.4 

50.00 

25.340 

115.008 

375.00 

15.261 

62.5 

400.40 

155.01 

314.1 

100.20 

6.3 

27.8 

1000.10 

4.75 

18.075 

25.50 

REVIEW  293 

Multiplication  Exercise 

328.  Multiply: 

1.  347  by  900  2.  568  by  36 

3.  425  by  17  4.  456  by  305 

5.  46,420  by  37  6.  $4.75  by  9 

7.  $0.85  by  24  a  $.026  by  136 

9.  $6,483  by  320  lo.  39.5  by  42 

11.  .036  by  500  12.  8.072  by  4000 

13.  5.672  by  8.2  i4.  .0375  by  .05 
15.  .0076  by  .082 

329.  Multiply: 

Multiplication  Exercise 


1. 

2. 

3. 

4. 

$25.65 

$69.75 

$172.50 

$67.58 

14 

213 

250 

182 

5. 

6. 

7. 

8. 

$96.47 

$84.55 

67 

881 

319 

86 

125 

2036 

9. 

10. 

11. 

12. 

475 

9423 

6987 

527 

86 

515 

484 

8643 

Division  Exercise 
330.    Divide : 

1.    38,642^8  2.    67,479 -^  9 

3.   25,800^60  4.    750,000-^-25,000 

5.    182,000^40,000        6.    90,750-^250 


294  INTERMEDIATE  BOOK 


7. 

42)365 

8.                    9. 

870           920 

10. 

6486 

11. 

1452 

12. 

38)6758 

13. 

4237 

14. 

60086 

15. 

42118 

16. 

79)55,869 

17. 

125,000 

18. 

640,050 

19. 

98,425 

20. 

152)5650 

21. 

8240 

22. 

36,472 

23. 

805,590 

24. 

.25)125.60 

25. 

$48.75 

26. 

$360.10 

27. 

$450 

28. 

68,429-^.025 

29. 

1326.14-^3.45 

30. 

80.742^375 

31. 

8.60^48 

32. 

$84.00^112 

33. 

365.702-^36 

34. 

.8386 -^  46 

35. 

72,862-^5000 

36. 

306,125-^2500 

37. 

3.649^28 

38. 

90.362 -^  .345 

39. 

6724.06-^3.32 

40. 

32,624.6-^.516 

41. 

8885^.85 

42. 

.36429^.035 

43. 

6305.5 -5- .007 

44. 

3460^.025 

Exercises  in  Fractions 
331.   Add: 


1. 

h^, 

hi- 

2. 

l>A> 

hi 

3. 

h  T5"?  12? 

1- 

4. 

h  is> 

A.i 

5. 

16f, 

25A 

671 

81|, 

12^. 

6. 

381, 

67f, 

72|, 

96|, 

46i, 

13|. 

REVIEW                               295 

Subtract : 

'•  l-l- 

8. 

i-A-        9-  l-A- 

10.   f-f 

11. 

A- 

■1-         12.  ^r-f- 

13.  31 -2f. 

14. 

n- 

■2|.        15.  61-1^. 

16.  8t-lf. 

17. 

H- 

If        18.  93-V-3I. 

19.  181-6^. 

20. 

27f 

-11      21.  671-83^. 

22.  16|-1|. 

23. 

25| 

-6f.     24.  469f-67|. 

25.  BW^-Q^%. 

26. 

46f 

-^.      27.  56^3^- 14|. 

Find  the  value  : 

28.   f  of  275. 

29.    1  of  416. 

30.    11  of  4800. 

31.   f  of  618. 

32.    320  x|. 

33.  4800  XjV 

34.    2800  xf 

35.    36,400x1*3-. 

36.    24.45  x|. 

37.   9.375 xf. 

38.    360x21 

39.   250  X  If. 

40.    450  x2f. 

41.   3401x12. 

42.    731x36. 

43.   2.48  X  If. 

44.    84.5  x2f. 

45.    16|x.8. 

Find  the  value: 

46.    25 -^f. 

47. 

16 

^f.            48.   i|^12- 

49.    25-^21 

50. 

16| 

Ki-     5x.  331^4. 

^52.    12f^60. 

53. 

40- 

+  8f          54.   8^4-5. 

55.  ,^v-f 

56. 

7i 

H-f.           57.   83J+6J 

58.   3.75^1 

59. 

.084 -)-f        60.   64.8^-1-. 

296  INTERMEDIATE    BOOK 

Combined  Fundamental  Processes 
332.   Perform  the  operations  indicated  : 
1.   2x6  +  8-4=  2.    18  +  6x4-1-3  = 

3.   24-j-3x6  +  8=  4.   11  +  6x2  +  8^4  = 

5.  27^3x4  +  6-7  = 

6.  2xl43-^6  +  8-17  = 

7.  78^13  +  26x4  = 

8.  65-9x4  +  16x2  = 

9.  (14x2)-16  +  2x4-^3  = 

10.  3  +  7x5^5x3  = 

11.  (2x8-4)^3  +  (30-8x3)-18-f-5  = 

12.  (235  -  78  -h  6)  - 14  X  11  -^  (186  -^31x2  +  5) 

-4  = 

13.  (2^  X  y)  +  "s^  6"~ 

14.  25^fx5i-|= 

15.  161^6  +  21-3^5x1  = 

16.  10xf^(fxfxi)-3A  = 


DENOMINATE  NUMBERS 


297 


DENOMINATE   NUMBERS 


333. 


Tables 


Linear 


12  inches  (in.  or  ") 


3  feet 

16.5  feet 

320  rods 

1760  yards 

5280  feet 

6086  feet 


=  1  foot  (ft.  or ') 
=  1  yard  (1  yd.) 
=  1  rod  (rd.) 
=  1  mile  (1  mi.) 
=  1  mile 
=  1  mile 
=  1  knot 


Liquid 
2  pints  (pt.)    =  1  quart  (qt.) 
4  quarts  =  1  gallon  (gal.) 

Dry 

=  1  quart  (qt.) 
=  1  peck  (pk.) 
=  1  bushel  (bu.) 
=  1  bushel 


2  pints  (pt.) 

8  quarts 

4  pecks 

32  quarts 

10  mills 
10  cents 
10  dimes 
100  cents 


Value 

=  1  cent  (f ) 
=  1  dime 
=  1  dollar  ($) 
=  1  dollar 


Time 


60  minutes  (min.)  =  1  hour  (hr.) 
24  hours  =  1  day  (da.) 

7  days  =1  week 

320  days  or  (wk.) 

12  months  (mo.)  =1  year  (yr.) 

Counting 

12  units  =  1  dozen  (doz.) 
12  dozen  =  1  gross 
30  units  =  1  score 

Weight 

16  ounces  (oz.)  =  1  pound  (lb.) 
100  pounds  =  1     hundred- 

weight 


2000  pounds 
2240  pounds 
7000  grains 


=  1  ton  (T.) 
=  1  gross  ton 
=  1  pound 


Angle 


90°  =  1  right  angle  (rt.  Z) 
180°  =  1  straight  angle  (st.  Z) 


Square 
144    square  inches  (sq.  iu)  =  1  square  foot  (sq.  ft.) 
9    square  feet  =  1  square  yard  (sq.  yd.) 

30 J  square  yards  =  1  square  rod  (sq.  rd.) 

'^'^    square  rods  =  1  acre  (A.) 

acres  =  1  square  mile  (sq.  mi.) 

Cubic 

1728  cubic  inches  (cu.  in.)    =  1  cubic  foot  (cu.  ft.) 
27  cubic  feet  =  1  cubic  yard  (cu.  yd.) 

128  cubic  feet  =  1  cord 


160 
640 


298  INTERMEDIATE  BOOK 

TESTS  OF  MATHEMATICAL  ABILITY  FOR  PUPILS 
OF  THE  FIFTH  AND  SIXTH  GRADES 

Written  tests  like  the  ones  proposed  below,  but  with  changes  in  the 
numbers  and  also  slight  changes  in  the  wording,  should  be  given,  with- 
out previous  notice,  limiting  the  time  to  15  or  20  minutes  and  requiring 
pupils  to  work  the  tests  in  the  given  order.  Assign  more  questions 
than  pupils  are  able  to  answer  in  the  given  time.  One  examination 
may  be  on  Part  I,  another  on  Part  II.  As  has  been  suggested  by  other 
writers,  either  or  both  of  two  systems  of  marking  may  be  adopted, 
(1)  marking  each  example  1  or  0,  according  as  it  is  right  or  wrong, 
or  (2)  marking  each  example  on  the  basis  of  the  total  number  of  steps 
involved. 

PART  I 

1.   Add     37.5  2.   Subtract  980651.19 

405.7  786438.255 

90.4 
3gQ  5  3.   Multiply  71.98  by  23.5. 

986.1  4.   Divide  17.89  by  3.5. 

Carry  answer  to  3  decimal 
places. 

5.   21  +  1+^-1  =  ?    6.    Multiply  5i  by  I  and 

7.  Divide  I  by  f.  simplify  the  answer. 

8.  Divide  lOf  by  4f .    9.    15  %  of  48760. 

10.   2.5%  of  178.65. 

PART  II 

1.  What  is  the  cost  of  eggs  a  dozen,  if  7  dozen 
cost  $  2.73  ? 

2.  A  locomotive  has  been  run  57  times  between 
Chicago  and  New  York.     If  the  distance  between 


TESTS  OF  MATHEMATICAL  ABILITY        299 

these  cities  is  908  miles,  how  many  miles  has  this 
locomotive  traveled  ? 

3.  Which  of  the  following  numbers  are  exactly 
divisible  by  6  :  46872,  176509,  37932  ? 

4.  A  loaded  truck  weighs  6J  T.  The  load  con- 
sists of  two  parts,  one  weighing  2^  T.,  the  other 
weighing  3|-  T.     Find  the  weight  of  the  truck. 

5.  The  weekly  wage  list  of  5  employees  is  $  27, 
$  30,  $  32,  $  29,  $  40.  What  is  the  average  wage 
per  week  ? 

6.  A  merchant  saves  $  475  a  year,  which  is  35  % 
of  his  earnings.     Find  his  earnings. 

7.  A  man  buys  40  ft.  of  garden  hose  at  9^i^  a 
foot,  discount  15%.     How  much  does  he  pay? 

8.  Find  the  interest  on  $  375  at  6  %  for  1  yr. 
and  6  mo. 

9.  Find  the  number  of  cubic  feet  of  space  2  ft. 
6  in.  long,  1  ft.  6  in.  wide,  and  1  ft.  5  in.  deep. 

10.    If  3  tons  of  coal  cost  $  14.25,  what  will  4 
tons  cost? 


Printed  in  the  United  States  of  America. 


T 


HE  following  pages  contain  advertisements  of 
a  few  of  the  Macmillan  books  on  kindred  subjects 


The  Health  Series  of  Physiology  and 
Hygiene 

By  M.  V.  O'SHEA 

Professor  of  Education,  University  of  Wisconsin ;  Author  of 
"  Dynamic  Factors  in  Education,"  etc.,  and 

J.   H.   KELLOGG 

Superintendent  of  the  Battle  Creek  Sanitarium ;  Author  of 
"  Man,  the  Masterpiece,"  etc. 

The  Health  Series  of  Physiology  and  Hygiene  presents  a  complete 
course  in  health  instruction  for  elementary  schools.  It  is  organized  con- 
veniently in  four  books  that  may  be  used  together  advantageously  and 
effectively  in  the  series.  Each  book  is,  however,  complete  in  itself,  and 
may  be  used  by  itself  in  courses  of  instruction  in  physiology  and  hygiene. 

Health  Habits.  The  purpose  here  is  to  establish  the  child  in  the  phys- 
ical habits  and  forms  of  conduct  that  make  for  bodily  health.  It  says  to 
the  child,  "These  things  are  desirable.     Can  you  do  them  in  this  way?  " 

Health  and  Cleanliness.  The  purpose  of  this  book  is  to  interest  chil- 
dren in  social  service  in  health;  to  show  the  dependence  of  health  and  well 
being  upon  protection,  and  especially  against  infections  through  germs, 
and  to  teach  children  what  to  do  for  themselves  and  others  in  case  of  an 
emergency. 

The  Body  in  Health.  The  human  body  is  here  presented  as  the  most 
remarkable  thing  in  nature,  in  the  variety  and  delicacy  of  its  action  and  in 
the  marvelous  adaptation  of  its  parts  and  functions.  It  presents  knowl- 
edge with  sympathy  and  it  leads  to  an  appreciative  understanding. 

Making  the  Most  of  Life.  This  book  directs  attention  to  the  chief 
factors  in  modern  life  which  reduce  the  vitality  and  the  health  of  people. 
It  is  a  forceftU  and  constructive  treatment  of  health. 


THE    MACMILLAN    COMPANY 

BOSTON  NEW  YORK  DALLAS 

CHICAGO  SAN  FRANCISCO  ATLANTA 


The  New  Sloan  Readers 

By  Mrs.   KATHERINE  E.  SLOAN 

Author  of  Primary  Readers 

Primer.     Cloth,  ismo,  colored  illustrations,  vi  and  122  pages.  $0.30 

The  First  Reader.     Cloth,  i2mo,  illustrated.  $0.80 

The  Second  Reader.     Cloth,  i2mo,  illustrated.  $0.35 

In  the  New  Sloan  Readers  the  author  plans  to  give  in  three  books 
a  basal  series  of  readers  that  attract  and  interest  the  child  through 
content  and  illustration,  and  that  give  to  the  child  in  the  most  direct 
way  and  in  the  shortest  time  the  independent  power  to  read. 

The  material  for  the  lessons  in  these  Readers  has  been  chosen 
from  the  best  sources  of  child  literature,  yet  so  taken  that  the  les- 
sons are  of  primary  interest  to  the  child  and  closely  connected  with 
his  daily  life  and  experience.  The  technical  drill  necessary  in  the 
teaching  of  reading  is  provided  in  charming  lessons  of  story,  rhyme, 
and  play  and  does  not  in  any  way  detract  from  the  interest  or  re- 
duce the  reading  value  of  the  lessons. 

The  method  employed  in  the  New  Sloan  Readers  is  based  upon 
the  thorough  presentation  of  the  simple  phonetic  elements.  The 
lessons  have  been  so  prepared,  arranged,  and  grouped  that  an  ade- 
quate preparation,  presentation,  and  drill  on  each  new  element  is 
provided.  The  phonetic  exercises  are  not  added  as  separate  exer- 
cises nor  presented  incidentally,  but  are  woven  in  a  simple,  natural 
manner  into  every  sentence. 

The  frequent  and  formal  reviews  bring  all  the  elements  to  the  at- 
tention of  the  child  at  opportune  times,  and  so  definite  progress  is 
made  in  all  the  work. 


THE    MACMILLAN    COMPANY 

BOSTON  NEW  YORK  DALLAS 

CHICAGO  SAN  FRANCISCO  ATLANTA 


Muscular  Movement  Penmanship 

By  C.  C.  lister 

Director  of  Penmanship,  Brooklyn  Training  School  for  Teachers 

Elementary  Book.    $0.16  Advanced  Book.    $0.20 

Teacher's  Manual  {Preparing) 

The  purpose  of  the  series  is  to  furnish  a  definite  plan  by 
which  practical  writing  may  be  taught  in  public  and  private 
schools  with  the  greatest  possible  economy  of  time.  In  the 
Manual  are  directions  for  the  teaching  and  supervision  of  writ- 
ing that  inexperienced  teachers  may  need  in  order  to  make  the 
work  interesting  and  productive  of  good  results. 

The  chief  features  of  the  treatment  are  correct  posture, 
movement,  and  good  form.  Throughout  the  series,  m  connec- 
tion with  each  lesson,  an  effort  is  made  to  establish  the  child  in 
habits  of  correct  posture. 

Correct  positions  of  the  body,  the  arms,  hands,  feet,  pen- 
holder, and  paper,  are  fully  illustrated  and  the  aim  has  been  to 
treat  the  matter  of  posture  concisely,  yet  so  clearly  that  there 
could  be  no  doubt  as  to  what  is  meant  by  correct  writing  habits. 
The  treatment  of  the  matter  of  posture  is  based  upon  facts  and 
conditions  in  writing  that  govern  the  health  of  the  whole  body 
and  the  special  organs  that  are  immediately  concerned  in 
writing. 

The  lessons  in  this  series  have  been  so  worked  out  that  a 
complete  system  of  exercises  for  the  development  of  muscular 
movement  writing  is  provided. 


THE    MACMILLAN    COMPANY 

BOSTON  NEW  YORK  DALLAS 

CHICAGO  SAN  FRANCISCO  ATLANTA 


English,  Spoken  and  Written 


By  henry  p.  EMERSON 

Superintendent  of  Education,  Buffalo,  New  York,  and 

IDA  C.   BENDER 

Supervisor  of  Primary  Grades,  Buffalo,  New  York 

Book  One.    Lessons  in  Language  for  Primary  Grades.     Clothy 

i2mo,  illustrated,  vii  and  217  pages.  $0.40x 

Book  Two.    Lessons  in  Language,  Literature,  and  Composition. 

Cloth,  j2mo,  illustrated,  xv  and  27g  pages.  $0.50x 

Book  Three.     Practical  Lessons  in  English,  Grammar,  and  Com- 
position.    Cloth,  1 2mo,  illustrated,  xiv  and ^yb  pages.  $0.60x 

The  title  of  this  series  is  significant  of  its  purpose  and  method. 
It  constantly  reminds  teacher  and  pupil  that  the  object  sought  is  to 
give  power  to  use  and  appreciate  English  in  oral  speech  and  written 
form  rather  than  to  limit  the  results  of  study  to  a  knowledge  of 
grammar. 

The  authors  have  aimed  to  make  the  series  practical  in  the  best 
sense  of  making  it  a  real  help  to  pupils  in  the  oral  and  written  use  of 
the  mother  tongue.  Instead  of  relying  upon  technical  grammar  to 
mold  the  daily  speech  of  children,  emphasis  is  laid  upon  practice  in 
speaking,  reading,  interpreting,  and  writing  under  the  guidance  of 
the  teacher. 

Throughout  the  book,  the  preeminent  importance  of  oral  practice 
is  recognized.  The  ear  is  too  often  a  neglected  factor  in  language 
teaching.  Selections  have  been  introduced  which  the  teacher  is  to 
read  to  the  pupils  to  train  them  to  a  perception  of  nice  language  val- 
ues. Pupils  are  directed  to  criticise  their  own  language  as  regards 
not  only  the  interest  of  the  thought  expressed  in  it,  but  the  quality 
of  its  sound  also. 


THE    MACMILLAN    COMPANY 

BOSTON  NEW  YORK  DALLAS 

CHICAGO  SAN  FRANCISCO  ATLANTA 


THIS  BOOK  IS  DUE  ON  THE  LAST  DATE 
STAMPED  BELOW 


AN  INITIAL  PINE  OF  25  CENTS 

WILL  BE  ASSESSED  FOR  FAILURE  TO  RETURN 
THIS  BOOK  ON  THE  DATE  DUE.  THE  PENALTY 
WILL  INCREASE  TO  50  CENTS  ON  THE  FOURTH 
DAY  AND  TO  $1.00  ON  THE  SEVENTH  DAY 
OVERDUE. 


SEP  25  mi\ 

'7  t94? 

StP8   1979 

I 

m 

-\'.t 

. 

LD  21-100m-7,'40(6936s) 

U.  C.  BERKELEY  LIBRARIES 


THE  UNIVERSITY  OF  CALIFORNIA  LIBRARY 


